Albert Barnes on Matthew 22:44

The Lord said, etc. This is the language of David. "Jehovah said unto my Lord"--the Messiah--" Sit thou," etc. This was a prediction respecting the exaltation of Christ. To be raised to the right hand of a king was significant of favor, trust, and power. Mt 20:21. This was done respecting Christ, Mk 16:19, Acts 7:55, Rom 8:34, Eph 1:20, Heb 1:3; 8:1, 10:12.

Thine enemies thy footstool. A footstool is that which is under the feet when we are sitting--implying that we have it under subjection, or at our control. So he shall put all enemies under his feet--all his spiritual foes--all that rise up against him, Ps 2:9,12 Heb 10:13, 1Cor 15:25.