In parallel sections, this psalm issues a summons to praise God, followed by reasons for doing so, calling us to worship and witness. It is among a group of "enthronement psalms" believed to have been used in the temple in Jerusalem in a yearly celebration of the reign of YHWH as king (see Psalms 47, 93, 97, 98, 99).
In the first half of the psalm, the assembled worshipers are commanded to sing songs of praise to God and to declare God's might and majesty among the nations (vv. 1-3). Why? Because of his exalted status and his royal excellencies (w. 4-6).
In the second half of the psalm, the scope broadens considerably. Now, the psalmist bids all peoples to extol God's glory and to bow in worship (w. 7-9). Indeed, the entire creation is to rejoice. Heaven and earth, the sea and its creatures, fields and forests— all are to be glad and sing for joy. Why? Because "YHWH is king" and because "he is coming to judge the earth" (w. 10-13).
This declaration that "YHWH is king" prefigures the central confession of our own faith, that "Jesus is Lord" (Rom. 10.9). Moreover, the joyful announcement of his "coming to judge the earth" likewise anticipates the arrival of Jesus as a baby in Bethlehem, as well as the second coming of Christ in power and glory. Although his kingdom has already begun, we are to eagerly await Jesus' return to set things right finally and fully, and to rule over alt in peace and love.
In the meantime we worship and witness. We express our joy by singing "a new song," the song of a Savior who gave himself on our behalf, and we witness to his reconciling love for all peoples.