Albert Barnes Commentary Daniel 4:22

"it is thou, O king, that art grown and become strong; for thy greatness is grown, and reacheth unto heaven, and thy dominion to the end of the earth." — Daniel 4:22 (ASV)

It is thou, O king - It is a representation of yourself. Compare Daniel 2:38.

That art grown and become strong - Referring to the limited extent of his dominion when he came to the throne, and the increase of his power by a wise administration and by conquest.

For thy greatness is grown - The majesty and glory of the monarch had increased by all his conquests, and by the magnificence which he had thrown around his court.

And reacheth unto heaven - An expression merely denoting the greatness of his authority. The tree is said to have reached unto heaven (Daniel 4:11), and the stateliness and grandeur of so great a monarch might be represented by language which seemed to imply that he had control over all things.

And thy dominion to the end of the earth - To the extent of the world as then known. This was almost literally true.