From left to right for classes, you have:
Warrior (Tank/DPS, both work very well)
Paladin (Tank/Healer/DPS, but playing any spec but Healer is 'meme tier' so most picking it will be Healer. Brings 5min duration buffs called 'Blessings', such as increasing attack power, increasing MP regen, or decreasing threat generated)
Hunter (3 DPS specs, gets a pet companion, very popular)
Rogue (3 DPS specs, star of many Warcraft AMVs back in the day due to being able to 100-0 someone in PVP before they can even get out of CC)
Priest (2 Healer specs and one DPS, will be played as a Healer mainly due to Shadow being 'meme tier' damage (though some raids run one Shadow just for the raidbuff it brings))
Mage (3 DPS specs, the best goldfarming class and one of the fastest at levelling, always popular)
Warlock (3 DPS specs, not as popular as Mage, but it can summon allies to their location with Ritual of Summoning, and in a game where you have to run to the dungeon entrance to enter it, that's pretty neat)
Druid (Tank+DPS/Healer/DPS specs, the Tank/DPS spec is a 2-in-1 and isn't completely terrible but most raids prefer to just have 2 Warriors as the tanks. The pure DPS spec goes OOM faster than a RDM on res duty, so it's a meme. The Healer spec is also a bit of a meme (due to being HOT focused, but the HOTs don't stack with other Druids unless you use different spell ranks), but it's the most functional of the three)