As Jesus was teaching in the temple area he said, "How do the scribes claim that the Christ is the son of David? David himself, inspired by the Holy Spirit, said: 'The Lord said to my lord, "Sit at my right hand until I place your enemies under your feet."' David himself calls him 'lord'; so how is he his son?"
The great crowd heard this with delight.
Questions come to mind, such as, "Erm, but the Christ is the son of David, right? The scribes are right about that, aren't they?"
Because Christ was coming to His Passion, He corrects a false opinion of the Jews, who said that Christ was the Son of David, not his Lord.
The Venerable Bede says that the Jews of his own time,
acknowledging that Christ is to come, assert that He is a mere man, a holy Person descended from David.
Jesus, then, correctly interprets the psalm as showing that the Christ will greater than David. The scribes are right to assign the title "son of David" to the Christ, but they interpret it backwards. The Christ is not honored by being the son of David; David is honored by being the father of the Christ.
This, perhaps, answers yet another question about the Gospel reading, viz, "If the great crowd heard this with delight, doesn't that mean the great crowd needs to get out more?" I mean, to be interested in a spot of exegesis is one thing, but to be delighted by it?
My cynical interpretation of the crowd's delight was that it arose from the discomfiting of the scribes, whom I assume (with little justification) weren't greatly loved by the common folk.
But now I can see how appreciation of the lesson Jesus is teaching -- Look! Your own inspired songs point to a Messiah Who is greater than you've been taught! You are awaiting, not merely David's son, but his Lord! -- could be a source of genuine delight proceeding from love of God.