To anoint means to choose by divine intervention. Or at least it seems like the big guy upstairs had something to do with it.
Saints and religious leaders are said to be anointed, but so is that new unstoppable quarterback who saved the team midseason. Anoint comes to us from the ancient Latin word unguere, which means "to smear." Which explains the other sense of this word, which is to apply with oil or another smearable substance, such as during a religious ceremony.