God is establishing His kingdom in the hearts of men and believers are sharing the Gospel with mankind to effect the work of God. Thy will be done on earth as it is in heaven. God's will is automatically and immediately done in Heaven and will be the same on Earth in time. It is God's will that all repent and come to know God. God's will is taught in His law.
Many rabbinic teachings are similar.
The sense is to defer to God. This is the sin nature, or iniquity, that conflicts with man's desire to do good, to do God's will. MAY YOUR WILL BE DONE , expressing an inward yearning. Give us this day our daily bread. There is much debate regarding the meaning of this phrase.