This represents the spiritual aspect of knighthood. Most of Arthur's knights are not able to achieve it, since they're too focused on worldly matters: harming others, drinking, and lust. The three knights who do achieve the Grail (Galahad, Percivale, and Bors) demonstrate purity, innocence, and correct theology.
The Grail ultimately represents the perfection of a knight's martial ability (knowing when to not harm others) and the perfection of his spiritual capacities. Once a knight achieves this kind of perfection, there's nowhere else for him to go, so he dies. Before you get bummed out, though, it's implied this is a good thing… because he gets to be with God.