Lovecraft was a horror author in the 20's. His influence is still very common today. Among his literary creations are the Necronomicon (as seen in the Evil Dead movies), Herbert West (as seen in the Re-Animator movies and the De-Animator Flash game here on Newgrounds) and many other things. The Lovecraft Mythos even inspired a two-part episode of Cartoon Network's Justice League.
Stephen King has made numerous nods to Lovecraft in many of his stories, including "the Lot" and "Needful Things". Indeed, countless horror authors have drawn upon his "Cthulhu Mythos" which has given it a life of its own - hence why so many people think the Necronomicon is a real book.
Among the movies made from Lovecraft's work (and there are over a hundred) such names as Vincent Price, Dean Stockwell, Lon Chaney Jr., Sandra Dee even Rutger Hauerhave all had parts in Lovecraft films. The first movie Francis Ford Coppolla ever worked on was a Lovecraft adaptation ("The Haunted Palace") even though he didn't get credit for his work editing the script.
Most of Lovecraft's work (almost exclusively short stories) are available on the web and a quick Google search should provide you with far more information than I should dump at you all at once.
The basic premise of most of his work is that there was another race of beings, the Great Old Ones, that ruled the Earth long before man and who will return to reclaim their world, when the stars are right.
That is not dead, which can eternal lie
And with strage aeons, even death may die
Hope that helps without being overwhelming.