As a guy who has read almost all of Lovecraft stories, played the roleplaying game, founded a rock band on Lovecraft's mythos, and based an art career on his monsters, I think I am qualified to chime in here.
I will try not to repeat too much information already provided, but I will try to dispel some of the misconceptions.
Cthulhu is one of the "Great Old Ones" who came to earth aeons ago, well before man evolved. Through some great cataclysm, his continent/city of R'lyeh was sunk beneath the waves and he has laid imprisoned therein ever since. At certain times, the stars become "right" allowing the city to come close or above the water's surface. Cthulhu's (psionic) power is picked up by sensitive human minds, and during these times they experience terrible dreams. One day, it is said in the fabled tome known as the Necronomicon, the stars will come right enough to truly free Cthulhu. Degenerate human cults around the world worship him, though whether this has any impact on Cthulhu isn't clear.
Common misconceptions are many. Cthulhu is portrayed sometimes as evil. Lovecraft specifically stated that Cthulhu is like a force of nature, and that concepts of good and evil are human vanities and have no bearing in the true nature of the universe. Contrary to many, it is my opinion that Cthulhu has no interest in mankind's doing, and is not looking forward to eating us all. He is not an organic living creature as we know it, and he has no interest in humanity any more than the average human is interested in vermin. Finally, contrary to some later stories, Cthulhu is not a water elemental nor is he associated with spirits, hell, and other human ideologies.
All that said, there is much more to learn. You can read the original "Call of Cthulhu" in a number of books, including my favourite "Bloodcurdling Tales of Horror and the Macabre
Additionally, the H.P. Lovecraft Historical Society has recently created a silent film adaptation of the story, which is quite good for a low budget feature. http://www.cthulhulives.org/store/store.lasso?1=product&2=8
Finally, for images of Cthulhu just google image or visit my profile on http://www.templeofdagon.com/artists/toren-macbin-atkinson/
(there are three Cthulhu images there, one in a Maurice Sendak style).
Ia Ia Cthulhu fhtagn!