From the introduction:
The Holy Grail War. A battle between 7 magicians, known as Masters, each with a summoned Servant representing some legendary figure of myth or history. For almost two centuries this battle has taken place in Fuyuki City, Japan. Originally set up by 3 great families of Magi, the tournament was a way for them to find a path to the source of all things. Or maybe it could grant any wish you might desire. Or maybe it's a way to bring the world to an end.
Things get a bit muddled over the generations, especially when you're as secretive as a Magician.