The first words of this psalm were the words on Christ's lips on the cross: "My God, My God, why hast Thou forsaken Me?" The crucifixion ended with a verse from Psalm 30--"Into Thy hands I commit my spirit"--so the thought arose in Christian sentiment, Fr. Patrick informs us, that while on the cross Christ silently recited all ten of these psalms. An excellent Great and Holy Friday exercise, imo.
Most notable are the exact descriptions of the crucifixion within this psalm, seen in vv. 7-8 (cf. Matt. 27:39-43), v. 15 (cf. Jn. 19:28) and v. 18 (cf. Jn. 19:23-4).
Fr. Patrick draws our attention to the quotation of this psalm found in the second chapter of the epistle to the Hebrews, where the Passion is given its proper context of "the Lord's sharing our flesh and blood so that 'through death He might destroy him who had the power of death' (2:14). Quoting Psalm 21 in this context of the Passion, the author tells us that Jesus 'is not ashamed to call them brethren, saying, "I will declare Your name to my brethren; / In the midst of the assembly I will sing praise to You"' (2:11,12)."
Appropriate that this psalm ends in the same manner as did our Lord's predictions of His crucifixion: with the victory of His Resurrection (cf. Mk. 8:31; 9:31; 10:34). "My spirit lives for Him; my seed will serve Him," the psalm declares. "The coming generation shall be herald for the Lord, declaring His righteousness to a people yet unborn, whom the Lord created."