The Shaman is a nice class that got many different styles of gaming that suit most people. You can do Healing with the Resto tree, Melee damage with the Enhancement tree and Spell damage with elemental. They used to be horde-only just like the Paladins used to be Alliance-only but with the release of Burning Crusade that change, and now in Cataclysm it changed again and most races can now choose to be a Shaman. They can wield every weapon in game, except for swords and they use Leather armor till they ding level 40 and from there and forwards they can and should use mail armor.
The Shaman class is commonly known for its ability to place out totems on the ground that boost themselves and the people in the same part as them, the totems give higher strength, higher agility, more MP5, it slows people and 1 totem can even stun other players, if it gets attacked. They got an ability that makes it possible for them to place 4 totems at the same time, instantly. This has made the Shaman class more popular that it was before and now you can see them in both the Alliance and the Horde factions.
Another thing that's associated with Shamans is their Blood Lust (Horde) and Heroism (Alliance) buff, which gives the whole raid, not just 5, but up to 25 people 30% increased melee/casting speed for 40 seconds. This is the single most important ability for raiding in large groups and every guild/raid/party is always looking for at least 1 Shaman, doesn't really matter what spec you are, they will invite you. They can summon Fire and Earth elementals which helps the party as well, it can tank for a short amount of time if you're not facing a raid boss.
The Shaman class got many different abilities that helps them during the 1-85 leveling time, one of these abilities is the Ghost Wolf. It will increase your movement speed by 40% and you can learn if from your trainer at the low level of 16. They can also ress themselves with the Reincarnation ability, but it does have a 1 hour cooldown. They can, just like priests/paladins, ress other players with no cooldown. They also have a Hearth Stone that's on 15 minutes cooldown,, their Astral Recall makes it possible to portal to where your hearth stone is currently set to.
The three different talent trees are just as I stated in the beginning, Elemental, Enhancement and Resto.
The Elemental tree is made for doing damage as a caster, they have some nice instant casts as well as Lightning bolt, shocks, totems etc. Their most known ability is the AoE one that throw people of bridges/elevators /middle of EotS (Eye of the Storm)
Enhancement is made for doing melee damage, their special attack are the wolves that fight at their side, stunning the enemies and healing the shaman.
And of course the Resto tree which is made for Healing both in PvE and PvP. Chain heals has become more popular in Cataclysm, hence Resto Shamas are more attractive to raid healing.