In PoE 2, Ascendancy Classes are choices to further specialize your Class. Other games may call is a Job Advancement, Subclass, etc.
Currently in Early Access, all 6 Classes have 2 Ascendancy Classes to choose from. It is planned for each Class to eventually have 3 Ascendancy Class choices.
You will be able to Ascend starting in Act 2, and each Ascendancy will have a special Passive Tree that will greatly empower your character.
Here's some quick notes on Ascendancy Classes:
You can get up to 8 points for the Ascendancy Tree.
You cannot change your Ascendancy.
You can refund/respec your Ascendancy passives on the tree. (Speak to The Hooded one or Doryani in town. It will cost Gold to refund)
It's not immediately clear how to Ascend in Path of Exile 2, so here's a quick breakdown of how to do it.
You Ascend by completing either Trial:
Trial of the Sekhemas
Trial of Chaos
There are 4 difficulty levels for each. Each difficulty level will reward 2 points. Each Ascension can be done with either Trial.
Your second Ascension is an exception, you can do difficulty 1 of both Trials to obtain 4 points. You will then need to complete the 3rd difficulty of either Trial for your 5/6th points.
First Ascension (2 Points)
Obtained From: Campaign Boss
Djinn Barya: Dropped from Balbala, the Traitor in Traitor's Passage (Act 2)
Inscribed Ultimatum: Dropped from Xyclucian, the Chimera in Chimeral Wetlands (Act 3)
Second Ascension (4 Points)
Obtained From: Random Monster Drop
Djinn Barya: Area Level 45+ Trials: 2
Inscribed Ultimatum: Area Level 60+ Number of Trials: 7
Third Ascension (6 Points)
Obtained From: Random Monster Drop
Djinn Barya: Area Level 60+ Trials: 3
Inscribed Ultimatum: Area Level 75+ Number of Trials: 10
Fourth Ascension (8 Points)
Obtained From: Random Monster Drop
Djinn Barya: Area Level 75+ Trials: 4, Defeat final boss
Inscribed Ultimatum: Defeat the Trialmaster (final boss)
How to Find Djinn Barya and Inscribed Ultimatum
In order to attempt each Trial, you will need to find the corresponding "key" to access the Trial.
Djinn Barya
In Act 2, you will encounter Balbala, the Traitor in Traitor's Passage. Defeating her will drop a "Djinn Barya" and unlock the Ascension Quest on your quest log.
From there, Djinn Baryas will be found randomly as a monster drop. You can then use these higher level Djinn Baryas to enter the Trial of the Sekhemas with higher difficulties.
IMPORTANT: If you fail the first Trial of the Sekhemas, you will still keep your Djinn Barya and keep retrying.
At higher difficulty levels, you will lose the Djinn Barya upon failing, and will need to find/use another Djinn Barya to try again.
Inscribed Ultimatum
Inscribed Ultimatums follow the same logic as Djinn Baryas. You will find your first one in Act 3 from Xyclucian, the Chimera in the Chimeral Wetlands.
Once again, you are allowed to fail the first difficulty and keep trying. From difficulty 2-4, you will lose your Inscribed Ultimatum upon failing and will need to find one again.
IMPORTANT: Most players find Trial of Chaos to be MUCH harder than Trial of the Sekhemas. It's not so bad early on, but for comparison, you can do your Third Ascension with a Level 60+ Djinn Barya vs a Level 75+ Inscribed Ultimatum.
Additional Tips
To close things off, here are some additional tips regarding the Ascension Trials.
Balbala, the Traitor
When fighting Balbala, she will occasionally disappear. The room will slowly fill with Poison Gas until you find her by walking around. When you find her, she will proceed to slam the ground around her, so be prepared to Dodge Roll away.
Xyclucian, the Chimera
When fighting Xyclucian, it will jump onto a stone pillar. Attack the stone pillar to break it. Xyclucian will fall down stunned, giving you a window of time to deal damage uninterrupted.
Trial of the Sekhemas
Trial of the Sekhemas is all about not getting hit. You have an Honour resource that goes down when you get hit, and losing all your Honour will result in a failed run.
Starting from Difficulty 2, (Area Level 45+) the Honour you lose ramps up drastically. To mitigate this, use Relics that have "Honour Resistance." This will greatly reduce the Honour damage you take from hits, letting you complete a run more easily.
Monsters in the Trial of the Sekhemas will drop Relics.
Trial of Chaos
The Trial of Chaos is generally difficult to complete for most characters. Don't underestimate the map hazards as they can quickly stack up and become very dangerous.
Unfortunately, some runs will present you with bad effects/debuffs that you just can't power through. With enough tries, you may get lucky some runs and pick tribulations that don't affect your build too much.
Overleveling
For many players, it's advised to overlevel before tackling the Trials. While you can start the first Trial of the Sekhemas early in Act 2, waiting until the end of Act 2 to level up more and get stronger can make the run much easier.
The same concept can be applied to Act 3 when you first gain access to the Trial of Chaos.
Similarly, you can tackle the third difficult of Sekhema (Area Level 65+) much later, even as far as level 75 or so.
This decision is ultimately up to you. As you play through the Endgame System, you'll find plenty of Djinn Baryas and Inscribed Ultimatums, so don't be too worried about failing.
Character Planning
Many players coming from PoE 1 expected the Ascension Trials to be easy. For many players, these Ascension points (outside of the first 4), are quite difficult to obtain.
When planning your character, don't expect to get your Ascension Points easily. If your character needs all 8 points to be strong, it will only make getting there more difficult.