The Pharisees expected a Messiah to be born in the lineage of David that would overthrow Rome and restore Israel as a nation. They did not understand the prophecies that foretold the Messiah’s divinity. This was the point that Jesus wanted to make with them, that the Messiah would not only be in the lineage of David, but also the Son of God. He was trying to open their eyes to see that He was in fact, the Messiah, the son of David and the Son of God.
When the Pharisees asked Jesus a question, their motivation was usually to entrap (Matt. 22:35) or otherwise show Him to be in error. However, when Jesus asked them this question about the Messiah, His motive seems to be not to stump them, although that was the apparent outcome, but to reveal His true identity to them.