By praying that God's will be done we are in effect telling our Father that we submit our will under His will. Even Jesus prayed "If it be possible, let this cup pass from me, not that my will be done but Yours" . Even Jesus Jesus had to submit His will to that of His/our Father. This is a daily prayer that I pray before I ever get out of bed:
Father, Guide me and show unto me everyone that you would have me help in some way today. Give me the words to say unto the world that will help its people not only know that You exist, but also, that will help heal any pain they may be feeling. Help me to not only know Your will but also to be able to do it and have the courage to do Your will regardless of who or what opposes my actions in coing your will in my life and community. Not that my will shall be done but that Your will may be done on Earth as it is in Heaven. Amen.
It's a simple prayer, I know, but, it tells God that I submit all of my life to Him and His will not only for my life but also for the whole world. That is why we are to pray that His will be done on Earth as it is in Heaven.