I think just a cursorily reading of the psalm leads us to understand that the psalmist is referring to the salvation of mankind. I believe we understand the tremendous importance of salvation, but let’s be truthful: We are thankful for the salvation Jesus has procured for us; I believe that we are extremely thankful; but it is not: “WOW!!! JESUS HAS SAVED US!!! OH! LET US SING A NEW, JOYFUL SONG!!!!!” Although the NAB puts it so clearly, “His right hand has won victory for him, his holy arm,” making it clear that His right hand has won victory for His holy arm, I was interpreting: He got the victory for us, for me. However, that is not what is being said. Let’s let St. Augustine explain it to us.
“The Lord hath done marvelous things.” What marvelous things? Hear: “His own right hand, and His holy arm, hath healed for Him.” What is the Lord’s holy Arm? Our Lord Jesus Christ. Hear Isaiah: “Who hath believed our report, and to whom is the arm of the Lord revealed?” His holy arm then, and His own right hand, is Himself. Our Lord Jesus Christ is therefore the arm of God, and the right hand of God: for this reason is it said, “hath He healed for Him.” (St. Augustine’s version of the Bible reads, I’m assuming, “His own right hand, and His holy arm, hath healed for Him,” instead of the renderings in the NAB and the RSVCE; however, it is the same: The victory is salvation, and salvation is the healing of sinful man.) It is not said only, “His right hand hath healed the world,” but “hath healed for Him.” For many are healed for themselves, not for Him. Behold how many long for that bodily health, and receive it from Him: they are healed by Him, but not for Him. How are they healed by Him, and not for Him? When they have received health, they become wanton: they who when sick were chaste, when cured become adulterers: they who when in illness injured no man, on the recovery of their strength attack and crush the innocent: they are healed, but not unto Him. Who is he who is healed unto Him? He who is healed inwardly. Who is he that is healed inwardly? He who trusteth in Him, that when he shall have been healed inwardly, reformed into a new man, afterwards this mortal flesh too, which doth languish for a time, may in the end itself even recover its most perfect health. Let us therefore be healed for Him. But that we may be healed for Him, let us believe in His right hand. You see, God has not saved us for ourselves. He has not saved us for our sakes, but His. God makes it so emphatically clear in Isaiah 43:25 when He says, “I, I am He who blots out your transgressions for my own sake”… The NAB renders it, “It is I, I, who wipe out, for my own sake, your offenses”… (emphasis added).
The LORD has made known His victory (salvation); He has revealed His vindication (triumph) in the sight of the nations. St. Augustine: “’The Lord hath made known His salvation. This very right hand, this very arm, this very salvation, is our Lord Jesus Christ, of whom it is said, ‘And all flesh shall see the salvation of God;’ of whom also that Simeon who embraced the Infant in his arms, spoke, ‘Lord, now lettest Thou Thy servant depart in peace; for mine eyes have seen Thy salvation.’ ‘The Lord hath made known His salvation.’ To whom did He make it known? To a part, or to the whole? Not to any part specially. Let no man betray, no man deceive, no man say, ‘Lo, here is Christ, or there:’ the man who saith, Lo, He is here, or there, pointeth to some particular spots. To whom ‘hath the Lord declared His salvation’? Hear what followeth: ‘His righteousness hath He openly showed in the sight of the heathen.’ Our Lord and Saviour Jesus Christ is the right hand of God, the arm of God, the salvation of God, and the righteousness of God.”
 Augustine of Hippo. (1888). Expositions on the Book of Psalms. In P. Schaff (Ed.), A. C. Coxe (Trans.), Saint Augustin: Expositions on the Book of Psalms (Vol. 8, pp. 480–481). New York: Christian Literature Company.
This theological reflection courtesy of the parishioners of St Paul Catholic Church in Pensacola, Florida: stpaulcatholic.net