3 “And he shall be like a tree planted hard by the running streams of waters”; that is either Very “Wisdom,” which vouchsafed to assume man's nature for our salvation; that as man He might be “the tree planted hard by the running streams of waters;” for in this sense can that too be taken which is said in another Psalm, “the river of God is full of water.” Or by the Holy Ghost, of whom it is said, “He shall baptize you in the Holy Ghost;” and again, “If any man thirst, let him come unto Me, and drink;” and again, “If you knew the gift of God, and who it is that asks water of you, you would have asked of Him, and He would have given you living water, of which whoso drinks shall never thirst, but it shall be made in him a well of water springing up into everlasting life.” Or, “by the running streams of waters” may be by the sins of the people, because first the waters are called “peoples” in the Apocalypse; and again, by “running stream” is not unreasonably understood “fall,” which has relation to sin.
That “tree” then, that is, our Lord, from the running streams of water, that is, from the sinful people's drawing them by the way into the roots of His discipline, will “bring forth fruit,” that is, will establish Churches; “in His season,” that is, after He has been glorified by His Resurrection and Ascension into heaven. For then, by the sending of the Holy Ghost to the Apostles, and by the confirming of their faith in Him, and their mission to the world, He made the Churches to “bring forth fruit.”
“His leaf also shall not fall,” that is, His Word shall not be in vain. For, “all flesh is grass, and the glory of man as the flower of grass; the grass withers, and the flower falls, but the word of the Lord abides for ever. And whatsoever He does shall prosper” that is, whatsoever that tree shall bear; which all must be taken of fruit and leaves, that is, deeds and words.
Source: The Enarrations, or Expositions, on the Psalms (New Advent)