For a long, long time I thought the phrase had a different meaning entirely. I thought it was pretty cool. Jesus was saying, 'I'm such a hardass, I don't care that you hit me. Here, have at the other side, too.'

Jesus the hardass. How cool.

But, no, that's not what it is. It could be the veiled political statement, like coffy said above. The way it is taken in our culture, though, is entirely different. It's thought to be a general pacifistic sentiment. It's usually interpreted to mean that it's okay for people to beat the shit out of you, and don't hit them back.

Anyone who's read any of my other nodes could guess I'm not thrilled with that interpretation. Sometimes force has to be taken to the aggressor, because that's all they understand.

Return force in kind, ten fold upon thine enemy. Force him to listen, and yeah, it will be good. Giveth the option: beat me, and be beat to hell; or sit, and speak, and listen, and think.
Say unto the world, Beat me at thine own risk! Show thy righteousness, for the arm of the righteous is indeed mighty. The righteous have the truth on their side, along with a fistful of quarters.
Book of Elwood Chapter 1, Verses 1-2

That's much more to my liking.