1 Chronicles 16:33

Then shall the trees of the wood sing out at the presence of the LORD, because he cometh to judge the earth.

The singing of the trees is personification, picturing unconscious and voiceless trees rejoicing before the Lord at His presence when He comes to judge the earth.
The words belong to the song David appointed for the bringing of the ark to Jerusalem, given in Hebrew poetry whose figurative language is not to be taken as literal prose.
His coming to judge the earth is cause for joyful singing and for giving Him glory, coming after the time of gospel offer when cases are examined and sentence is given and executed.
The song charges God's people to declare His glory and salvation among the nations by His works and by His Word, that Gentiles might be converted and share one law with Israel as His priest to the world.
The passage gives Psalm 96 in revised form, while its opening answers to Psalm 105:1-15 linking the keeping of His commandments to a thousand generations.

Text, Setting, and Language

The verse belongs to the psalm David gave to be sung when the ark was brought from Kirjath-jearim to Jerusalem, in the setting of the ark's return and David's gladness.
The passage in 1 Chronicles 16:23-33 contains the whole of Psalm 96 in a revised and somewhat altered form with slight variations.
The chapter is parallel with Psalm 105, with 1 Chronicles 16:8-22 containing the first fifteen verses of Psalm 105, where the keeping of God's commandments is connected with a thousand generations.
The chapter is Hebrew poetry, not prose, and its expressions are figurative poetic diction that must not be construed literally as prose statements are construed.

The trees singing out is personification, in which inanimate trees without consciousness or voice are pictured as singing before the Lord at his presence when he comes to judge the earth, in the manner of other biblical images in which inanimate things are made to speak or act.
That personified singing stands with the blood of Abel crying, the stone hearing, the trees holding an election, the thistle proposing marriage, the stone crying out of the wall, the defrauded hire crying, dead Abel yet speaking, the souls under the altar crying, and death and hades riding and being cast into fire.
Together these prove that God makes lifeless and unconscious things speak and act concerning the facts of their case, and therefore the speeches of the dead in hades — Rachel weeping, Pharaoh comforted, dead kings mocking Babylon, and Dives and Lazarus conversing — are the dead personified as though alive, after God's manner of calling those things which be not as though they were.

Judgment and Worldwide Proclamation

The trees of the wood are pictured as responding with joyful singing at the presence of the Lord because he comes to judge the earth, so that his judgment is set forth as a cause for rejoicing and not for dread. Their singing with joy before him belongs with the call to give God glory in view of that coming judgment. That coming to judge the earth follows the close of probation, after the time in which God offers life and the gospel is proclaimed, when judgment brings examination of cases, then sentence, then execution of sentence.

The verse stands within the charge of 1 Chronicles 16:8-36 for Israel to declare Jehovah's glory among the nations, that is among the Gentiles, in order that the Gentiles might be converted. God gave his truth to Israel not for themselves alone but that the whole nation might be his priest to the world, and when people from the nations give themselves to God one law is for both Jew and Gentile. Cited as part of that call to proclaim his glory among all nations, the verse upholds the calling of God's people to make his glory known.

The same passage shows that God's salvation was to be proclaimed throughout the world through his works and through his Word. That proclamation was to go to all the world both in his works and by his Word, showing that the gospel had already been preached world-wide in the past.