The guy who is supposed to be the supervisor in the grail war, he's the priest that no one likes. Shiro is hostile to him from the beginning, and swears he won't return unless absolutely necessary. It turns out that Kirei fought against Shiro's mentor Kiritsugu in the last grail war. While both survived, they hated one another. Kirei especially hated Kiritsugu's philosophies which Shiro has vowed to continue. As the mediator in the grail war, he's still compelled to help Shiro, and finds his problems amusing.
Kirei seems unpredictable, but as his character develops through the stories, it turns out he's very consistent. From a young age, Kirei found pleasure in nothing. He attempted to lead a virtuous life by becoming a priest like his father, but was never able to find fulfillment. Eventually he discovered something disturbing: he only finds happiness in the misery of others. While Kirei offers people help, this usually comes at the price of suffering down the road. Kirei doesn't really have any desire for the grail in the way of granting a direct wish, but might have other nefarious uses for it.
Kirei appears to be an evil person, but in some ways he's the opposite. Despite being sadistic, he never openly inflicts suffering on others. Kerei is utterly dutiful to the church, and while it seems ironic such a person would be a member the institution, Kerei obeys the creed of the church quite well. His willingness to seek redemption for his black heart over the years shows an odd conviction to do the right thing even if it's against his nature. In RPG terms you could say Kirei is the incarnation of lawful evil.
We are the same, you and I. As we do not have clear wishes, we cannot seek salvation.