Classes? Let's see...

Warrior: Armor. Weapons. Likes to kill things. Doesn't cast magic at all, but does have special abilities powered by "rage". This class can have a hard time soloing in my experience, but every "good" group wants one.

Paladin: Alliance characters only. A lot like the warrior, but can't wield any weapons with range. Also, can cast some magic - mostly heals and buffs. Also has auras which can buff the entire party. Easier time soloing thanks to the heals, but you'll find a lot of paladins think they're invincible....which they aren't.

Shaman: Horde characters only. A melee class that uses magic in a multitude of ways. Buffs, damage spells, heals, and can even drop totems which also serve multiple functions. Can't wear armor as heavy as an equal level warrior, but does get to take "saptas" which make you see things. Weird things.

Rogue: Last of the melee classes, and also the absolute kings of single target damage. Ability to stealth, open locks, and other generally thief-like things. Despised by a great many other players in PvP because they tend to attack from behind and win.

Hunter: Ranged damage class. Likes to use bows or guns, but can also fight in close respectably. Also, gains the ability to tame wild animals and have them help in future fights. Due to players not paying attention to their pets while in a group, this class has developed a somewhat undeserved reputation of being group "unfriendly".

Druid: The jack of all trades. A caster to begin with, but will learn to shapeshift into multiple creatures as time goes on. Bear form can function as a warrior, cat form as a rogue, etc. Well played druids are forces to be reckoned with, but that can be a steep learning curve.

Mage: The powerful wizard. Retains the polymorph ability they are famous for from Warcraft 2, and a plethora of offensive spells. Gains the ability to teleport to many locations later in the game.

Priest: The healer. Blizzard wanted to break the mold of healer classes established in other games, so you'll actually have offensive spells. Not as powerful as a mage, despite the popular opinion, but your healing ability is second to none which makes you harder to kill. Thanks to the mage-like damage rumor, no longer the least played class in the game. Every group wants one, but they also like to blame you when they get themselves killed.

Warlock: The only class that can actually kill itself. Wait, that sounds bad. Um, I'm actually not certain how to describe these guys. Wielders of dark magiks, summoners of demons, warriors in cloth. Yeah, they're that weird. Makes them least likely to be invited into a group. I've managed to do some things as one that I wouldn't even think to try as another class though.

Some funny slogans I've heard --
Warriors do it the hard way.
Paladins can do it all day.
Hunters do it with their pets.
Rogues do it from behind.
Druids do it all kinds of ways.
Mages do it with sheep.
Priests do it with God.

Warlocks: The best class for killing invisible monsters underwater. <-- One day, I bet we find one.

As to the game being fun... Every race has a dance they can do. Female humans do the Macarena. Male Night Elves dance like Michael Jackson. Female Night Elves do ... you should see that one. Male Undead headbang. Male Orcs dance like MC Hammer, which I've used numerous times after beating truly difficult enemies to my groups great amusement. So yeah, it's fun. Much more so when you get to play with friends.