Fate/stay night was originally a visual novel with H-scenes. The movie itself is an adaptation of one of the 3 routes of the visual novel. From watching it, it heavily relies on the fact you know the characters and such ahead of time since it doesn't do much to develop them. You'd probably get more enjoyment if you've watched the anime that came before the movie (it adapted the Fate route from the visual novel).
Anyways if you do enjoy it, I'd highly advise you too look up the VN. It has been completely translated to English by a bunch of fans. I called it a VN with H-scenes earlier because it mainly revolves around it's story and the H-scenes are more or less tacked on. In fact, the game was ported to PS2 later on with the H-scenes removed and there's a patch with the English translation by another group that replaces to H-scenes with the PS2 alternative. Basically the premise for the H-scenes is nothing more than "we can recharge your mana by having sex".