O Radix Jesse, qui stas in signum populorum, super quem continebunt reges os suum, quem gentes deprecabuntur: veni ad liberandum nos, jam noli tardare.
O Root of Jesse, which standest as a sign to the peoples, at whom kings shall shut their mouths, whom the gentiles shall beseech, come to deliver, delay thou not!
Here are the corresponding modified hymn verses from "Veni, Veni, Emmanuel" and "O Come, O Come Emmanuel."
Veni, O Jesse Virgula: Ex hostis tuos ungula, de specutuos tartari Educ, et antro barathri. R: Gaude! Gaude! Emmanuel, nascetur pro te Israel!
Come, O Rod of Jesse: from the clutches of the enemy, from the snares of hell, and from the depths of the netherworld lead forth thine own. R: Rejoice! Rejoice! O Israel, to thee shall come Emmanuel!”
Jesse was the father of David and a descendant of Judah, Jacob, Isaac and Abraham. God chose Jesse (and his youngest son, the shepherd David) as recorded in this Scripture: "And the Lord said unto Samuel ... Fill thine horn with oil and go; I will send thee to Jesse, the Bethlehemite, for I have provided me a king among his sons" 1 Samuel 16:1. Bethlehem, where Jesus was born, is also called the city of David.
Isaiah, the prophet, wrote this about 300 years later, "And there shall come forth a rod out of the stem of Jesse, and a branch shall grow out of his roots; And the spirit of the Lord shall rest upon him, the spirit of wisdom and understanding, the spirit of counsel and might, the spirit of knowledge and the fear of the Lord" Isaiah 11:1-2.
This prophecy refers to the coming Messiah as the "rod out of the stem of Jesse" and as a "branch" that will grow out of Jesse's roots. By the use of the Hebrew word, netzer, for branch, the prophecy even went so far as to specify the place where Messiah would live, in a play on words. The town Natzeret [Nazareth] is the word netzer plus the feminine ending. "And He came and dwelt in a city called Natzeret (Nazareth), that it might be fulfilled what was spoken by the prophets" Matthew 2:23.
The hymn refers to Jesus as the rod of Jesse unlike the O antiphon, which refers to Jesus as the "root of Jesse." Radix Jesse is the term used for the Messiah in another prophecy from Isaiah, "In that day there shall be a root of Jesse who shall stand for an ensign [a sign] to the peoples" Isaiah 11:10.
Also unlike the hymn, the O antiphon refers to the part of the prophecy that foretold that the Messiah would be a standard bearer who will attract the Gentiles and that the Messiah would deliver His people, "And He shall set up an ensign for the nations, and shall assemble the outcasts of Israel, and gather together the dispersed of Judah from the four corners of the earth." Isaiah 11:12.
Here is Dom Gueranger’s commentary about this O antiphon for December 19.
"At length, O Son of Jesse! thou art approaching the city of thy ancestors. The Ark of the Lord has risen, and journeys, with the God that is in her, to the place of her rest. 'How beautiful are thy steps, O thou daughter of the Prince,' [Cant. vii. 1.] now that thou art bringing to the cities of Juda their salvation! The Angels escort thee, thy faithful Joseph lavishes his love upon thee, heaven delights in thee, and our earth thrills with joy to bear thus upon itself its Creator and its Queen. Go forward, O Mother of God and Mother of Men! Speed thee, thou propitiatory that holdest within thee the divine Manna which gives us life! Our hearts are with thee, and count thy steps. Like thy royal ancestor David, 'we will enter not into the dwelling of our house, nor go up into the bed whereon we lie, nor give sleep to our eyes, nor rest to our temples, until we have found a place in our hearts for the Lord whom thou bearest, a tabernacle for this God of Jacob.” [Ps. cxxxi. 3-5.] Come, then, O Root of Jesse! thus hid in this Ark of purity; thou wilt soon appear before thy people as the standard round which all that would conquer must rally. Then, their enemies, the Kings of the world, will be silenced, and the nations will offer thee their prayers. Hasten thy coming, dear Jesus! come and conquer all our enemies, and deliver us.'
Here is a link from New Liturgical Movement that includes a link to a sound file of the chant.
See "History and Mystery: The O Antiphons in a Favorite Hymn" for my post on the relationship between the O antiphons,"Veni, Veni, Emmanuel" and "O Come, O Come Emmanuel."