"Thy Will be done,
on Earth as it is in Heaven."
Here we enter into mystery. Jesus is teaching us to pray that what the Father wishes to happen will, in fact, happen. It stretches our understanding enough to include the idea of the Father's will not being some monolithic force moving in time and space to bring things to pass. There are, apparently, some things that occur that are not His will, and there are, apparently, some things that are His will that don't occur. And we are given the opportunity to partner with Him in the reducing of the number of those things. The prayer for the accomplishing of God's will is a prayer that puts us fully in the flow of His work in the world. And not just as an interested bystander, but as an active participant.
We have made the determination that this prayer answered will be better than this prayer not answered. That God's will being done on earth will be better than any of the alternatives. This is a prayer on the way to Kingdom coming and centers on what is here and now. We align ourselves with God's desires. Some of them are so clear and known that we may pray more specifically. We may pray that we become more like Jesus. That is the Father's will for all His children. We may pray for the salvation of persons, for we know that God is not willing that any should perish. We may pray that the Lord of the Harvest would send out laborers into His harvest field, for we have it on good authority that that is precisely what He desires as well.
But some of what the Father wants is not so clear or precise. We pray as if looking through a darkened glass - listening deeply to hear the whispers of His will in this situation or that - praying as we sense the Spirit blowing this way or that. Always bring our prayer to the heart of the Father for correction or direction - we do not insist that what we want becomes His will, but that what He wants becomes ours.
The locus of this prayer is the only place we know of in the universe where it is not already so. It is here on earth that choices were made to set aside His will. And so, it is here on earth that we pray, "May your will be fully accomplished."