What are shamans?
Shamans are the Horde-only class, designed to be healer/warrior/mage hybrids. Generally, we have spells and abilities taken from those base classes combined into one class. We also have totems which add a variety of effects, from group buffs to debuffs and attacks.
The class itself is a complex class that has one of the more varied amount of spells and effects present. Shamans are the most versatile class in WoW.
The official page describing shamans is here: http://www.worldofwarcraft.com/info/classes/shaman.html