What is the meaning of Matthew 5:31-32?

31 It hath been said, Whosoever shall put away his wife, let him give her a writing of divorcement: 32 But I say unto you, That whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery: and whosoever shall marry her that is divorced committeth adultery. (Matthew 5:31-32 KJV)

William Burkitt’s Commentary

Our blessed Saviour still proceeds in vindicating and clearing the seventh commandment from the corrupt glosses of the Pharisees. Almighty God had tolerated the Jews, in case of uncleanness, to put away their wives by a bill of divorce, De 24:1

Hereupon the Pharisees maintained it lawful to put away the wife upon every slight occasion. This abuse Christ corrects; and shows that divorce, except in case of adultery, is a certain breach of the seventh commandment.

Learn, 1. That so indissoluble is the marriage-covenant betwixt two persons, that nothing but adultery, which violates the bands of marriage, can dissolve or disannul it.

Learn, 2. When persons are unjustly put away, it is unlawful for them to marry to any other, or for others knowingly to marry to them.