It completes what has been joined socially, emotionally and spiritually. It is the final step, a step blessed by God when in the right context. I don't know if you caught the emphasis in the reading from 1 Corinthians 6. The basic point there is that our bodies are more than a mere chunk, maybe a very good looking chunk, but a mere chunk of flesh. If that's all they were, then to join two bodies is no big deal.
Animals do it all the time.
But human sexuality is much deeper than that. There's a spiritual dimension to it. We who are gathered here are temple beings. We've got the Holy Spirit of God dwelling inside. That makes our bodies very holy, sacred places.