Both. The processor is what runs the game, the graphics card is like a separate processor whose purpose is to take the load off of your computer. Normal computers that come with on board graphics will have a harder time processing everything going on with your computer and the game itself, where graphics cards are optimized to basically run the game itself. If you're looking at buying a computer get something with an i7 processor and at least an Nvidia g700+ series, like a 765 isn't bad. I'm fairly sure that's what I have an I can play WoW on ultra graphics on a high populated server and get 90+ fps.
