Without giving away any spoilers, the story is that every forty years (supposedly), seven masters, usually proficient in the arts of magic, gather in Japan at the city of Fuyuki, and essentially fight to the death in an a battle royal, and whoever wins gets possession of the grail, which can grant their greatest desires. The twist here is that every Master gets a servant, a heroic spirit, who's identities usually are people who have existed in history, whether they be real or fictional (Alexander the Great, Gilgamesh, Hercules, etc.), and they also have their own reasons for wanting to win the grail war, and this mutual desire between servant and master can either create synergy or tension between the two. Fate/Zero takes place during the fourth Grail War, in the 1990s, and it's a prequel to Fate/Stay Night (the anime adaptation of which was, as many people who have watched it will tell you, incredibly average, which is putting it lightly).