Jesus tightens up the earlier version (Matthew 5:32), which has more words but makes the same point. This is a "punchier" version of the same line. Getting to the point, adultery, much quicker. Here the man who remarries another woman is defiled, or because the verb could also be the middle voice, "defiles himself." The phrase "except that it be for" is two words that mean "not upon" that, together, have the sense of "not in the case of."
The uncommon word here means "fornication" for a man and "prostitution" for a woman, but the sense is sexual immorality in general. Jesus only uses this word three times.
Christ's Words in Matthew as a Guide to 40 Days of Prayer.