We are to pray, "Thy will be done on earth AS IT IS IN HEAVEN." (Mathew 6:10) How is God's will done in heaven? Let me mention four things.
First of all, the angels are in a perpetual state of WAITING UPON GOD for His commands. They don't run around heaven trying to do `something for God' according to their own ideas. No. They wait for God to speak first - and only then do they act.
"I'm looking for one who will wait and watch
For My beckoning hand, My eye -
Who will work in My manner the work I give,
And the work I give not, pass by.
And oh the joy that is brought to Me
When one such as this I can find -
A man who will do ALL My will,
Who is set to study his Master's mind"
So, when we pray "Thy will be done on earth as it is in heaven," it means, first of all that we want to hear what God has to say to us.
Secondly, when God speaks, the angels obey IMMEDIATELY. They don't say "Lord, I'll wait a few days and think about it. I want to find out what my fellow angels think about this." There's no such thing in heaven. When God has spoken, that is final. Obedience is immediate.
Our prayer then should be, "Father, help me, that I don't delay when I hear Your voice. I don't want to rush ahead of Your time, but once You have spoken I want to obey immediately."
Then thirdly, when God commands something in heaven, it is done COMPLETELY. Those angels don't go out and obey God partially. Our prayer therefore should be, "Father, help me to do ALL your will in my life - to obey every commandment completely, whatever the cost."
And finally, the obedience of the angels is JOYFUL. They are not grudging and complaining in their obedience. No angel compares his task with another's and says, "Lord, why have You given me a more difficult task than You've given that angel" etc.,
We hear such complaints even among believers, "Why should I make all the sacrifices? What about him/her," etc., But we never hear such words from the angels in heaven. They consider it a privilege to do anything for God and they rejoice at every opportunity to obey Him.
And so when we pray this prayer, we are asking that God's will may be done in our lives like that - joyfully and without any complaints and without any comparisons with others.