What is meant by "Thy will be done on earth as it is done in heaven"?
The words, "Thy will be done as it is in heaven," are taken from the Lord Jesus' model prayer in Matthew 6:10 and Luke 11:2.
Jesus was teaching His disciples how God the Father wants people to pray. This wasn't Jesus' own prayer, because He had no sin for which to be forgiven, as the prayer requests. Jesus' own prayer is found in John, all of chapter 17.
"Thy will be done on earth as it is in heaven", is the recognition that God deserves all honor and glory. It expresses recognition that God's is always the right direction to follow, no matter the circumstances in which we as human beings find ourselves. Proverbs 3:5-6 is an excellent guideline for us to follow in this regard.