Turn The Other Cheek

To understand the principle Jesus is getting at, we must understand both the summary that He gives as well as all the examples:

Summary: "Do not resist an evil one"
The significant term here is "resist". It is used in different contexts, but often in the context of rebelling against an authority. Thus, it might be translated as "do not rebel" or "do not stand against the authority". It is used in this way in Ephesians 6 when we are told to "stand against" or "resist" the devil. Thus, we are told in one place to resist, but in another place not to. Of course, this fits Jesus' example who did not resist arrest, but constantly resisted Satan and the demonic authorities.

Examples:
Whoever slaps you on your right cheek, turn the other to him also.
In the ancient world it is a common punishment for an authority to slap his underlings. Masters slapped slaves, fathers slapped children, guards slapped prisoners and magistrates slapped (or had slapped) anyone who was under their authority in a court situation. To "turn the other cheek" is to offer oneself to be slapped more. In the context of an authority, a single slap would be considered acceptable, even a just punishment. But if one was slapped again, it would be oppression and an acceptable situation for an appeal. Jesus, in the trial before Annas, was actually questioning the justice of being slapped at all. This is what the turning the other cheek is doing as well, questioning the righteous judgement of the authority. If they give into it and slap you again, they have proved their unrighteousness.

If anyone wants to sue you and take your shirt, let him have your coat also.
Those whom were owed were considered the authority over those who were in debt. The one who is owed had the right to throw the other into prison (see Matt 18). According to the law, there were strict guidelines as to how much a debtee could receive from a debtor. The debtee could not put the debtor into danger, by, for instance, taking his coat overnight (Exodus 22:26-27). Should a debtee take too much so as to threaten the life of the debtor, then the debtor can cry out to God and God would judge the debtee. Thus, inviting a debtee to take one's only covering is to invite the debtee to display his unrighteousness and so be judged.

Whoever forces you to go one mile, go with him two.
In the ancient world, a Roman soldier had the right to "volunteer" any non-citizen of Rome to carry his pack for a mile. But the law is strict about it being only one mile. Should the Roman insist upon two miles, then he would be judged. This is offering a soldier to do injustice according to the law and so be judged by the law.

Give to him who asks of you,
and do not turn away from him who wants to borrow from you.
Roman soldiers could also take possessions from non-citizens. These possessions are to be "borrowed", but often they never came back.

All of these examples are legal oppressions. A magistrate has the right to slap. A debtee has the right to take clothes from the debtor. The soldier has the right to have one carry his pack or to take the possessions of a non-citizen. These are all oppressions and they ar all legal, according to human law. The point here is to not only accept the legal oppression, but to go extra in creating a super-legal situation. The law covers a single slap, a coat, a single mile. But Jesus is saying that the oppression must be obvious, beyond recognition.

Why? Because if we resist the evil authority for the legal oppressions, then we are rebellious and we will deserve what punishments we get. But if we are in a place where we are being punished to the extreme and we don't deserve it, then God will step in. God is interested in justice and will step in if injustice is done. So Jesus is recommending creating a situation of obvious oppression to which we may appeal to God (as stated in Exodus 22), and God will step in, take away the oppressor and give us justice (Luke 18:1-7, and Mark 12:1-9)