'Putting away' is mostly translated as divorce. My understanding of this is that, in OT times men could divorce their wives with relative impunity, for various reasons. But Jesus said that it should not be so. Matthew 19:9 & 5:32 suggests that divorcing an adulterous wife is acceptable; but other than this, it seems that Jesus is saying that marriage should be taken more seriously - and that attempting to divorce for other reasons is breaking a solemn vow (acting treacherously).