A Character Class defines a skill set that you pick for your character. Once picked this can't be changed, but all roles in (Tank, Heal, DPS) can be performed on any of the classes (some classes are optimum for some roles though).
All classes can be played with either Stamina based skills or Magica based skills depending on your weapons and play-style. A full list for all skills for each class can be found at ESO-Skillbook.com.
Do you like to stab people from the shadows? Then the Nightblade may be for you. This is a challenging class to play but is very effective in PvP as a sniper. In PvE the natural fit for this role is as DPS with a focus on single-target end-fight executes.
DKs are naturally good Tanks, with skills that give armour to themselves and the group, as well as abilities to pull enemies into damage provided by the DPS.
Sorcerers are focused on doing up-front area damage in a group and have a natural fit for DPS. Magica Pet Sorcs are very effective for end-game builds and Stamina based sorcs are fantastic PvP builds and PvE DPS.
Sorcs can also heal, though are perhaps not optimum for end-game PvE healing.
The Magica Templar is a natural fit for a healer in ESO, though is also a very effective DPS as well.
The Stamina Templar is a good PvP DPS build, especially with 2H weapons.
Wardens were introduced with Morrowind Q2 2017 and currently can be purchased as an option with Crowns.
Wardens are another healing option, but with a specific focus on buffs and de-buffs for the group.
Stamina Wardens are lethal option in PvP and can be very effective DPS in PvE.
Necros were introduced in Q2 2019 with the Elsweyr expansion. At this stage it's too early to tell which role will best suit the Necro. They are currently only available with the purchase of the Elsweyr chapter.
SHARED SKILL LINES
These skill lines are available to all characters and are combined with the class skills to make your build. This means everyone can play a little differently, and adds to the flexibility in roles.
The Fighters guild has skills that can add flexibility to Stamina based classes, including skills that can pull enemies to the player, adding "chain" functionality to more than just DKs.
This skill line is leveled by killing undead and daedra.
The Mages guild has skills that can add flexibility to Magica based characters. Most of the skills in this line are DPS focused.
This skill line is leveled by finding and "reading" lorebooks around the world.
The Undanted skills are provide a ranged taunt and resource regenerating skills, as well as a number of other helpful skills, focused on PvE dungeons and trials.
This skill line is only leveled doing dungeon and trial content.
The Psijic guild was introduced with the Summerset chapter. It introduces a number of skills that add flexibility to all roles.
This skill line is only leveled doing the Psijic quest-line.
There are three, mostly passive, skill lines for each armour type, but the active skills can fill in gaps that may be missing due to the character class you've chosen.
Vampires are created by being bitten by another vampire player or a natural vampire. The skill line is particularly suited to Magica DPS players.
Werewolfs are created by being bitten by another werewolf player or a natural werewolf. The skill line is particularly suited to Stamina DPS players.
Even if you focus on PvE, there are a number of essential skills in the Alliance Warfare lines for Healers and Tanks, such as Purge and Warhorn. This skill line is only leveled through doing PvP content.