For the Lord most high - Yahweh, the Most High God; that is, who is exalted above all other beings. Compare Exodus 18:11; 1-Chronicles 16:25 Psalm 96:4; 2-Chronicles 2:5; Psalm 95:3.
Is terrible - literally, is to be feared; that is, reverenced and adored. There is an idea in the words "terrible" and "terror" which is not contained in the original, as if there were something harsh, severe, stern, in his character. The word in the original does not go beyond the notion of inspiring reverence or awe, and is the common word by which the worship of God is designated in the Scriptures. The meaning is, that he is worthy of profound reverence or adoration.
He is a great king over all the earth - He rules the world. He is a universal Sovereign. The immediate "occasion" of saying this, when the psalm was composed, was evidently some victory (which had been achieved over the enemies of the people of God) so decided, and so immediately by the divine power, as to prove that he has absolute control over all nations.

For the Lord most high is terrible - He has insufferable majesty, and is a great King - the mightiest of all emperors, for he is Sovereign over the whole earth.

For the Lord most high is terrible,.... Christ is not only the Son of the Highest, but he himself is the most high God, God over all, blessed for ever. He is higher than the highest, than the angels in heaven, or any of the sons of men on earth. He is the high and lofty One, that dwells in the high and lofty place. And even this character agrees with him as the ascended Lord and King in his human nature; he is ascended on high, is set down on the right hand of the Majesty on high. He is highly exalted to be a Prince and a Saviour; he is made higher than the heavens, and than the kings of the earth are; angels, authorities, and powers, are subject to him. And this is a reason exciting all the people to joy and gladness. And he is "terrible" to his enemies, being the Lion of the tribe of Judah; who will rule the nations with a rod of iron, and break them in pieces as a potter's vessel: and so he will be when he shall come in the clouds of heaven, land descend from thence, in flaming fire, to take vengeance on those who have despised and rejected him; and at the same time will be glorious to and admired by them that believe in him. His appearance, which will be terrible to others, will be matter of joy to them. Though the word used may be rendered as it is in Psalm 111:9; "reverend" or "to be feared" (b), as he is; see Isaiah 8:13; both on account of his goodness, as the Redeemer and Saviour of his people, Hosea 3:5; and of his greatness, being equal with God, and King of saints. As it follows;
he is a great King over all the earth; as he must needs be, since he is the great God and our Saviour; and is King of kings, and Lord of lords. He is now King of Zion, and head over all things to the church; and before long the kingdoms of this world will become his, and he will take to himself his great power and reign, and shall be King over all the earth openly and visibly; he shall be one, and his name One, Zac 14:9; which is another reason for joy and gladness among the people.
(b) "reverendus", Junius & Tremellius; "timendus est", Coccius; "venerandus", Michaelis.

His universal sovereignty now exists, and will be made known.