However, a more historical context to Jesus' words can be made. In the culture Jesus was speaking in, it was common for Roman soldiers, or others in authority to strike a lower-class person's face with the back of the hand as a display of dominance and authority. The right hand was always used, just as when they performed a Roman salute with their right arm, etc.
Apparently, the left hand was never used for anything but "unclean" purposes, and as such was never equated with power and authority like the right hand was. The bible talks exclusively about God's right hand too, so there is something to the concept of power being in the right hand.
Therefore, if the striker could only use the back of his right hand, when the other cheek was turned it would not be an option for him to strike the victim again with the back of his left hand.
I don't know if Jesus' purpose was to protect his people from getting hit more than once, or maybe more likely it was a way for the victim to nonviolently stand up to the authority of the striker and take away his perceived control over him. But without it looking like a direct defiance of the assailant's authority, because the victim was in all appearances looking like he was submitting.
Either way, we are called to be peace makers and to love our enemies.