This is one of a group of songs that announce and praise the kingly rule of God. Many contain the sentence "The Lord is king" or something quite like it (Psalms 93; 95; 96; 97; 99), which has caused many scholars to think they were sung at a festival (perhaps in the fall) announcing anew God's enthronement and celebrating God's rule. Whether or not that is true, this group of psalms does give praise to God as the ruler and righteous judge of all the earth.
God's rule deserves to be celebrated, precisely because God alone judges with complete righteousness and equity (v. 9). So, everyone and everything sings praises, plays lyres, trumpets, and horns, and makes a joyful noise before the Lord (vv. 4-6). Even the sea roars, the floods clap their hands, and the hills sing for joy. Under righteous rule, everything prospers (people and all creatures), so everything joins in praise.
1 O sing to the Lord a new song,
for he has done marvellous things.
His right hand and his holy arm
have gained him victory.
2 The Lord has made known his victory;
he has revealed his vindication in the sight of the nations.
3 He has remembered his steadfast love and faithfulness
to the house of Israel.
All the ends of the earth have seen
the victory of our God.
4 Make a joyful noise to the Lord, all the earth;
break forth into joyous song and sing praises.
5 Sing praises to the Lord with the lyre,
with the lyre and the sound of melody.
6 With trumpets and the sound of the horn
make a joyful noise before the King, the Lord.
7 Let the sea roar, and all that fills it;
the world and those who live in it.
8 Let the floods clap their hands;
let the hills sing together for joy
9 at the presence of the Lord, for he is coming
to judge the earth.
He will judge the world with righteousness,
and the peoples with equity.
New Revised Standard Version Bible: Anglicized Edition, copyright © 1989, 1995 National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved worldwide. http://nrsvbibles.org