Verse 31 is a quote from Genesis 2:24 and the first marriage between Adam and Eve. Husband and wife would become one flesh – as if two souls inhabiting one body. This ancient thought was firmly planted in the Jewish mind of the time, and even Jesus quoted it in His teaching. One man, one woman, for life was the concept, and anyone who stepped outside these bounds was severely punished (especially the women).
But as with many concepts in the Old Testament, the New Testament believers through Christ and the Spirit came to understand that marriage actually referred to a deeper meaning which was previously concealed. The true meaning is that marriage is a metaphor for the relationship between Christ and the church being joined in one body with Him as the head.
As humans we need metaphors and concrete examples to understand abstract concepts. That’s one reason Jesus taught so often in parables. One man, willing to do anything possible to protect and show his love for his wife, a living image of Christ’s sacrifice and love for the church, is joined to one woman, willing to submit and put her husband first, a living image of the church’s relationship to Christ. Both are constantly thinking of the other and living with the other’s best interest at heart. That's the deepest meaning of marriage. It's meant to be a living drama of how Christ and the church relate to each other. "As God made man in His own image, so He made earthly marriage in the image of His own eternal marriage with His people" (Geoffrey Bromiley).
“According to the Bible, the marriage act is more than a physical act. It is an act of sharing. It is an act of communion. It is an act of total self-giving wherein the husband gives himself completely to the wife, and the wife gives herself to the husband in such a way that the two actually become one flesh.” ~ Wayne Mack