In a literal interpretation (as depicted in the film The Big Fisherman), if a person has been slapped in the face by another as an insult or provocation to a quarrel, a Christian ought not to respond by hitting back or otherwise responding hurtfully. Rather, he ought to present the other cheek (the one that has not been slapped yet) and offer to let that cheek also be slapped in the hopes that the other person's conscience would be pricked and would not slap it, thus preventing a quarrel from really getting started.
However, the phrase is almost always used in the metaphorical sense.
See: Sermon on the Mount
wikipedia.org dumped 2003-03-17 with terodump