The questioner was trying to set Jesus up.  If he had answered the question directly, he would have condemned himself as one inciting rebellion against Rome, or as one opposed to the law of God.  By distinguishing between that which belongs to God and Caeser, he disarmed the question.  At the same time, he didn't evade it because the point was made that if one is going to live under the protection of governing authority, then they are to render to the power the support it claims to do its job as long as it doesn't interfere with following higher duty.