Psalm 132:17 There will I make the horn of David to bud: I have ordained a lamp for mine anointed.
A horn represents a powerful offspring and refers to Jesus Christ.
Luke 1:69 And hath raised up an horn of salvation for us in the house of his servant David;
To bud means to grow.
There refers to Zion in Jerusalem.
Jesus will restore the kingdom of David as the kingdom of God when he returns.
He will reign over the earth from the throne of David in Jerusalem.
Luke 1:32 He shall be great, and shall be called the Son of the Highest: and the Lord God shall give unto him the throne of his father David: 33 And he shall reign over the house of Jacob for ever; and of his kingdom there shall be no end.
A lamp means that his line will not be extinguished, that he will always have a descendent to sit upon his throne.
1 Kings 11:36 And unto his son will I give one tribe, that David my servant may have a light alway before me in Jerusalem, the city which I have chosen me to put my name there.
1 Kings 15:4 Nevertheless for David’s sake did the LORD his God give him a lamp in Jerusalem, to set up his son after him, and to establish Jerusalem:
2 Chronicles 21:7 Howbeit the LORD would not destroy the house of David, because of the covenant that he had made with David, and as he promised to give a light to him and to his sons for ever.
David’s ultimate descendant is Jesus Christ who is also a light to the gentiles.
Luke 2:30 For mine eyes have seen thy salvation, 31 Which thou hast prepared before the face of all people; 32 A light to lighten the Gentiles, and the glory of thy people Israel.
I hope you find this helpful.