Our

A personal relationship- I am His child. ( My needs- God is personal; He is concerned about me and my needs!)

Father

 A family relationship- He is my Father. (I can cry out to Him 'Daddy' - Abba)
Rom.8:15 For you did not receive the spirit of bondage again to fear, but you received the Spirit of adoption by whom we cry out, "Abba, Father."
Jesus had this kind of relationship. See also
Mk. 14:36 And He said, "Abba, Father, all things are possible for You. Take this cup away from Me; nevertheless, not what I will, but what You will."

which art in heaven

A humble, yet exalted, relationship- I pray from earth.
PS.113.4-6
Psalm 113:4-6 God humbles Himself to behold us or notice our prayers.
The LORD is high above all nations, His glory above the heavens. [5] Who is like the LORD our God, Who dwells on high, [6] Who humbles Himself to behold The things that are in the heavens and in the earth?
Application: Every prayer heard of God is an example of the humility display of God- for me when I dislike His call to me to be humble and receptive to His will for any issue of life.

ADORATION -- The First Prayer Principle
Hallowed be Your Name -- God wants to be set apart from all others. 
God wants us to ‘set His name apart’ from all other things in order to please Him.
Hebrews 6:6 But 1)without faith it is impossible to please Him:
for he that cometh to God must believe 2) that He is,
and 3) that He is a rewarder of them that diligently seek him.
Without faith we cannot know who God is and what He does because He cannot be seen with the mortal eye.
Hebrews 11:1 Now faith is the substance of things hoped for, the evidence of things not seen.
The two ways to have faith are
1) to believe that "He Is..." The verb here is "being," "to be," that is "to exist." In other words, we have to trust in the fact that God does exist with a recognizable character even though He cannot be seen nor His existence proven.
2) to believe that "He is a rewarder..." This means that He does Works that reward those who exercise faith in Him.
He Is -- describes His Attributes, and thus is the first sub-category of 2 for this prayer principle.
He is a rewarder -- describes His Works, the second.