What is Parry?
Parry is a skill granted by all bucklers (pure evasion shields). Shields that have armour will not grant the parry skill and will instead grant 
Raise Shield.
Parry is a channeled skill. While channeling parry, you will hold up your shield to block incoming attacks. If an enemy hits you from the front with a strike or projectile attack (or certain other attacks) while you are standing in melee range and channeling parry, you will block all damage from the incoming attack and retaliate with a swipe of your shield. This swipe deals physical damage based on the evasion rating of your shield (3 to 4 added physical damage per 5 evasion) and has a 400% more stun buildup multiplier and cannot be evaded (meaning no accuracy is required for parrying otherwise evasive mobs). The swipe can hit multiple enemies at once if they are standing close enough together.
Parry does NOT require precise timing. You can simply hold down the parry button as long as you want before getting hit by an attack, and as long as you are 1) in melee range, 2) facing the enemy, and 3) don't get stunned, you will parry the attack (assuming it is a parriable attack, more on that later). That said, your heavy stun bar will build up each time you get hit while holding down parry and will not decrease until you have stopped holding parry for a few seconds, so don't hold it forever or you will eventually get knocked down!
While holding down parry, you will never avoid taking a hit entirely through block or evasion, it will always connect; however, block and evasion (as well as all your other passive defenses) will be considered when determining how much stun buildup you receive. It is very helpful to have defenses like evasion, armour, and increased stun threshold so you don't get instantly stunned trying to parry larger attacks. Note that stun threshold is based on your maximum life, so simply getting more life (or strength) is also a good way to get stunned less often. I highly recommend using Steadfast I support on parry to increase your stun threshold.
The Parried Debuff
Hitting an enemy with parry's swipe attack will apply the parried debuff. This debuff makes enemies take 50% more damage from attacks and lasts for 2 seconds by default. You can increase the duration of the debuff with the "increased parried debuff duration" mod, found on passive tree nodes such as 
Off-Balancing Retort, as well as with generic skill effect duration modifiers, such as Prolonged Duration II. You can also find "increased parried debuff duration" on emerald jewels. The "more attack damage taken" portion of the debuff can also be increased by the "increased parried debuff magnitude" mod, found on nodes such as Reprisal. As of patch 0.4, taking all the "increased parried debuff magnitude" nodes on the tree will make the debuff grant 104% more attack damage taken.
Skills such as 
Disengage, 
Fangs of Frost, and attacks supported by Frenzied Riposte can consume the parried debuff in order gain various additional effects.
Some unique bucklers interact with the parried debuff:
Dunkelhalt grants 50% increased parried debuff magnitude at the cost of taking 50% of the damage of the blocked hit
Nocturne makes the parried debuff apply to spell damage taken instead of attack damage, and also increases the duration by 100%
Silverthorne applies 10 stacks of critical weakness (aka +5% chance to be crit) to parried enemies
Calgyra's Arc grants 50% increased parried debuff duration as well as infinite parry range
Parry Hitboxes
Parry has two separate hitboxes. The first is called parry range, and determines the area where the enemy can hit you in order to block the attack, as well as how far away from the enemy you can be. It is a conal hitbox in front of your character, and slightly offset to the right side where you hold your shield. Parry range can be increased by nodes on the tree like Resolute Reprisal, as well as Calgyra's Arc. With infinite parry range, you can parry enemies from across the screen regardless of distance and still hit them and apply the parried debuff. However, even with infinite parry range, the shield swipe will still only hit other enemies if they are in melee range.
The second hitbox, called parry hit area of effect determines the area where your shield swipe hits enemies in front of you. Only "increased parry hit area of effect" modifiers, such as Reverberating Parry, can increase this area. With a large enough parry hit area, you can hit multiple enemies at once with the swipe and apply the parried debuff to all of them. Note that Parry does NOT have an AoE tag, and therefore cannot scale with generic area of effect modifiers or area damage.
Despite not having a strike tag, parry still works with 
Tribal Fury to splash the damage and debuff to nearby enemies. You can also use 
Tyranny's Grip in your main hand while parrying and it will splash the same as tribal fury. Because the splash itself is an AoE, you can scale the splash with AoE modifiers even though parry's swipe does not normally work with these modifiers.
What can I parry?
When fighting bosses, many boss abilities can be completely interrupted by parrying, making it a very powerful tool if you know how to use it. For example, dangerous attacks like the freezing beams called down by Count Geonor or Doryani's spinning butt lasers can be parried. But it can be difficult to know what you can and cannot parry without trial and error.
In general, you can (almost) always parry:
- Strikes - simple attacks where the enemy swings a weapon or arm at you from the side
- Projectiles - any projectile attack is generally parriable as long as you are standing in melee range. This includes mortar type attacks as well as forward-firing projectiles.
- "Breath" attacks - any attack that involves breathing fire or some other element on you, or that resembles a flamethrower is usually parriable (these attacks do many rapid small hits, not damage over time)
- Ground area effects - any ground effect that hits you, such as the exploding pods in a ritual or Asinia's exploding curse circles, are usually parriable if you are standing next to an enemy when you get hit by them. Also includes attacks where enemies like The Devourer pop up out of the ground.
- Volatile orbs - any orbs that chase you around and explode when you touch them are usually parriable. This includes things like the chaos orbs from volatile plants rare modifier.
You may or may not be able to parry:
- Leaping/Falling attacks - some attacks that involve a monster leaping or falling on you can be parried, some cannot. For example, in Geonor's first phase when he turns into a wolf and falls on you from the sky, you can parry it, but in his second phase after he turns into the corrupted wolf/human hybrid his falling attack cannot be parried. Crowbell's leap slam attack cannot be parried.
- Slam attacks - attacks that involve slamming an arm or weapon down on you from above may or may not be parriable. The Bloated Miller's overhead slam attack is parriable, as are Doryani's arm slam attacks in his second phase. Lachlan's red flash ground slam that releases a shockwave across the ground is not parriable, but his slams in front of then behind him are parriable.
- Charging/rolling/thrusting attacks - The Queen of Filth's rolling slam cannot be parried, but the Mighty Silverfist's rolling attack can be parried. The Bloated Miller's charging attack cannot be parried except for the final hit at the very end of the charge. Count Geonor's sword thrust attack and his sword charge in his first phase cannot be parried.
- Beams/lasers - many of these can be parried if you are close to the boss, but some cannot. The lightning beams that Jamanra puts on the ground and the ones that dance around the arena can be parried. So can Doryani's spinning butt lasers.
You typically cannot parry:
- Non-Projectile "Rain"/Dropping attacks - attacks that involve raining or dropping something other than the monster's own body on you usually cannot be parried. This includes Asinia's bone storm when she traps you in her bone prison, as well as Captain Hartlin's anchor drop attack. Note that this only applies to non-projectile attacks, whereas projectile mortar attacks like Candlemass's fire mortar or The Rotten Druid's projectile barrage are almost always parriable.
- Damage over time - anything that doesn't hit you but instead does damage over time (like a ground degen) cannot be parried
This is not an exhaustive list and it definitely requires some trial and error to learn which attacks can and cannot be parried. There are some exceptions to these rules (such as The Bloated Miller's backhand strike attack, which cannot be parried for some reason).
If you want to learn more about exactly which attacks can and cannot be parried, you can check out the monster's page in PoE2DB and look at the individual skills. Any non-projectile skill that has an "Area" tag at the top (not to be confused with "is area damage" at the bottom) is NOT parriable unless it also has a projectile tag. Also, any skill that has the line "base skill cannot be avoided by dodge roll or evaded or blocked" or "base skill cannot be blocked" is also NOT parriable. Everything else, as long as it's not damage over time, should be parriable.
Other Parry Interactions
There are quite a few other useful things you can do with parry besides just preventing damage. Here are a few:
- Parry has a 400% more stun buildup modifier. Pin I support converts this stun buildup into pin buildup, making parry very good for pinning enemies. You can combine this with Bone Shrapnel support on Disengage or any other follow-up skill for big pack-clearing explosions. Similarly, you can use Brink I support on parry and Impact Shockwave on Disengage to make overlapping explosions from heavy stunning enemies. You can also use
Kaltenhalt to make parry freeze instead of stun, and deal cold damage. - While it is not tagged as a strike skill, parry works with Tribal Fury and Tyranny's Grip to splash the damage and debuff to nearby enemies. This allows you to apply the parried debuff to entire packs and trigger many overlapping shockwaves with Disengage or Fangs of Frost.
- You can put your buckler on your second weaponset and automatically swap weapons when parrying. This allows you to take parry-related clusters on the tree on your second weaponset while leaving your first weaponset available for damage. It also means you can use anything you want in your mainhand of your second weaponset as a "stat stick" to buff parry. Some good options are a
Construct Hammer to allow parry to daze enemies, any wand with "damage gained as extra" modifiers (which will apply to parry's damage), or a sceptre for extra spirit. - If you have extra spirit available, you can use
Tame Beast and find a beast with the "Trail of Lightning" modifier and set it to only be on your parry weaponset. This way the beast will spawn right next to you whenever you parry and will immediately drop shocked ground under the enemy. Then, when you use a follow-up attack with your main weaponset, the beast will be unsummoned so it doesn't die. - The parried debuff increases all attack damage taken by the enemy, even if you aren't the source of that damage. This makes it a good option for minion/companion builds, as well as multiplayer support characters.
- Parry synergizes nicely with several spirit skills.
Magma Barrier will grant some additional block chance and cause a fiery explosion when you parry, dealing additional damage based on your shield's evasion. 
Wind Dancer triggers an explosion around you when you parry. 
Iron Ward will store physical damage prevented while parrying (which means the entire hit since parry prevents all damage taken). You can then use Iron Ward to do a large physical damage explosion that hits the entire screen.
