This refrain is repeated three times in this psalm (Ps 80:3, 7, 19). It is a prayer repeated for emphasis as Asaph processes the pain of the remnant of Israel's people and remembers her past with God.
The psalm starts with an appeal to the God of Israel, focusing on the unique relationship that God has alone in covenant with His people (Ps 80:1-3). It then moves on to how God had rightly judged them for their lack of obedience to that covenant, focusing on the ridicule that Israel faced from the surrounding nations in the humility of the aftermath of Babylon's sack of Jerusalem (Ps 80:4-7). It is a somber and clear stating of the facts.
Then the bulk of the psalm paints a word picture common in the Old Testament to describe God's sovereign care for Israel: the nation is His vineyard. The poetry recounts Israel's founding as a vine brought out of Egypt and planted by God. He cultivated it until it thrived to shade mountains and stretch from the Sea to the River. Yet now it had been trambled and burned. The final call is for God to restore the glory and vitality of His people again (Ps 80:8-19).
Sometimes when our lives are broken, a season in which our hearts cry out for restoration is what we must know. It is what God wants of us in that season. The heart that looks for God to restore and to rebuild has real hope and strength. It is drawn to God and He will not let such cries go unheeded by His love.