“and to give us a peg in his holy place.” Ezra here uses an illustration from the culture in which he lived and that would have been clear to the people. Houses, and even tents, had “pegs” in the wall or posts to hang things on that kept things orderly and secure so they would not be kicked around on the floor (and most floors were dirt floors). Ezra refers to a “peg” in his holy place, in the new Temple that they had permission to build.
Nebuchadnezzar had destroyed the Temple that Solomon had built, and Israel had been without a house for God for decades, which implied that God could not live among His people. Now it seemed that God would soon once again have a dwelling place among His people, and in the very spot where He had chosen to live. The fact that God would once more be among His people in His house was a “peg” that the people could cling to and draw strength from.