What does Matthew 1:6 mean?

So far, Matthew has traced the genealogy of Jesus from Abraham to Jesse, the father of King David. David serves as a milestone in both Jesus' ancestry and the history of Israel. He reigned during the golden age of the nation, and God promised that his descendants would sit on the throne of Israel forever. Israel longed for the Messiah to come and return Israel to the independence and triumph of those days. Even in his opening genealogy, Matthew is showing that Jesus is that long-expected king.

Matthew follows Jesus' line through Jesse to David and then to David's famously wise son King Solomon by a woman he calls "the wife of Uriah." Matthew could have left her out of his telling of the line of Jesus or he could have simply called Solomon's mother Bathsheba. Instead, he intentionally forces his readers to remember David's darkest sin and how it led to the birth of Solomon. The story, told in 2 Samuel 11—12, is a tale of sexual immorality and murder. King David had sex with Uriah's wife while Uriah was at war. She became pregnant. When David's schemes to cover up the illegitimate pregnancy failed, he had Uriah killed and married his widow. The son of that initial union died, but after his death Bathsheba became pregnant with Solomon. Second Samuel 12:24–25 says, "And the LORD loved him and sent a message by Nathan the prophet. So he called his name Jedidiah, because of the LORD."

One reason Matthew may be emphasizing these illicit and complicated relationships that led, eventually, to the birth of Jesus, is to show that God used one unconventional circumstance after another through sinful human beings to bring His greatest blessing to humanity by His own will.