I'm not talking about the Priests and Paladins we see in World of Warcraft, Everquest 2 and probably lots of other games I haven't played. Religion for character classes like these is more often than not a game mechanic, something which is used to explain the source of their powers.
Divine Magic is a term which is frequently used to explain a player or character's ability to cast spells. It's a catch-all term, attributing magical and mystical abilities to ill-defined deities and otherwordly beings watching over the game-world. Usually benevolent, these beings empower their followers, enabling them to carry out miraculous feats.
Probably deliberately, religion has remained generally fuzzy and ill-defined in MMOs. That shouldn't come as much of a surprise. Religious debate in the real world is a sure-fire way to incite some flames, and it's no wonder that games developers have been keen to shy away from it thus far.