From Barnes' Commentary on Isaiah 9:7:
"Upon the throne of David - See the note at Acts 2:30. This was in accordance with the promise made to David; 1 Kings 8:25; 2 Samuel 7:12-13; Psalm 132:11. This promise was understood as referring to the Messiah. The primary idea is, that he should be descended in the line of David, and accordingly the New Testament writers are often at pains to show that the Lord Jesus was of that family; Luke 2:4. When it is said that he would sit upon the throne of David, it is not to be taken literally. The uniqueness of the reign of David was, that he reigned over the people of God. He was chosen for this purpose from humble life; was declared in his administration to be a man after God's own heart; and his long and prosperous reign was a reign over the people of God. To sit upon the throne of David, therefore, means to reign over the people of God; and in this sense the Messiah sat on his throne. There is also a similarity in the two administrations, in the fact that the Messiah was taken from humble life. and that his reign will be far-extended and prosperous. But the main idea of resemblance is, that the reign of each extended over the people of God.
And upon his kingdom - That is, over the kingdom of the people of God. It does not mean particularly the Jews, but all those over whom the divine administration should be set up.
To order it - To raise up, or confirm it. The word, also, is sometimes used to denote to found a kingdom. Here it means to confirm it, to cause it to stand."