In the New Testament, the first four verses of Psalm 110 are quoted or alluded to 33 times. This was researched by David Hay and Dr Thomas Constable reports this finding in his Bible commentary.

Of the four Gospels, three of them record Jesus as quoting Psalm 110:1. The way Jesus quoted this scripture was designed to challenge the hearers over their preconceived notion regarding who the Christ was. He challenged them to reflect on the divinity of the Christ and the position designated to Him as Lord. The apostle Matthew records the circumstance in which Jesus quotes Psalm 110:1.

Here's the passage citing Psalm 110:1 as it appears in Matthew,

41 While the Pharisees were gathered together, Jesus asked them,

42 saying, “What do you think about the Christ? Whose Son is He?” They said to Him, “The Son of David.”

43 He said to them, “How then does David in the Spirit call Him ‘Lord,’ saying:

44 “The Lord said to my Lord, ‘Sit at My right hand, Till I make Your enemies Your footstool’”?

45 If David then calls Him ‘Lord,’ how is He his Son?”

46 And no one was able to answer Him a word, nor from that day on did anyone dare question Him anymore.

Mat 22:41-46 - NKJV

Among the Pharisees, no one was able to answer Jesus’ closing question as it is recorded in that passage above. They were not able to answer because no one among them was willing to answer Him. To answer would have got them in a tangle of their own making and demonstrated the inadequacy of their understanding of who the Christ was.

Let's return to the question He opened with, “What do you think about the Christ? Whose Son is He?” At the beginning, the Pharisees were quick to answer that isolated question when He posed it. However, once He pointed out to them that David called the Christ ‘Lord’ in Psalm 110:1, no one among them wanted to answer His closing question.

What was Jesus seeking to draw out the recognition of regarding the Christ? Whose Son (given the way Jesus handles this scripture) do you think Psalm 110:1 points out Christ as being? I think you have to reach the same conclusion as all the apostles came to, namely, that Christ is the Son of God!

Here then is the explanation in regard to what you are declaring when you say, “Jesus is Lord". To make the declaration "Jesus is Lord" is to declare Him the Lord spoken of in Psalm 110:1 where it says,“The Lord said to my Lord.” It is in effect to say that Jesus the Christ is the Son of God, the Second Person of the Godhead.