Matthew 22:41 While the Pharisees were gathered together, Jesus asked them, 42 Saying, What think ye of Christ? whose son is he? They say unto him, The Son of David.43 He saith unto them, How then doth David in spirit call him Lord, saying, 44 The LORD said unto my Lord, Sit thou on my right hand, till I make thine enemies thy footstool? 45 If David then call him Lord, how is he his son? 46 And no man was able to answer him a word, neither durst any man from that day forth ask him any more questions.
Jesus is showing the Pharisees that although the Christ (Messiah) is descended from David (and therefore called the son of David), he must in some respect be greater than David because David (who had the Holy Spirit) called him Lord.
Here he is quoting Psalm 110:1
Psalms 110:1 « A Psalm of David. » The LORD said unto my Lord, Sit thou at my right hand, until I make thine enemies thy footstool.
A son cannot normally be considered greater than the father who begat him.
The conclusion they should have drawn from Divid's words is that Christ must be the Son of God in order to be greater than David.
This is clearly prophesied:
1 Chronicles 17:11 And it shall come to pass, when thy days be expired that thou must go to be with thy fathers, that I will raise up thy seed after thee, which shall be of thy sons; and I will establish his kingdom. 12 He shall build me an house, and I will stablish his throne for ever. 13 I will be his father, and he shall be my son: and I will not take my mercy away from him, as I took it from him that was before thee: 14 But I will settle him in mine house and in my kingdom for ever: and his throne shall be established for evermore.
Luke 1:32 He shall be great, and shall be called the Son of the Highest: and the Lord God shall give unto him the throne of his father David: 33 And he shall reign over the house of Jacob for ever; and of his kingdom there shall be no end.
Jesus was descended from David through his mother Mary, but his Father was God. – which the Pharisees should have understood.
I hope you find this helpful.