It’s plural. When Jesus’ disciples asked him how to pray, he put the words of a collective prayer on their tongues. He instructed his followers to address their Father as a family.When I think of the "our" part, I think of how sad some Protestants have it. No, really. I don't mean to pick on them, (okay, I do), but the relationship I have with Jesus isn't just about having a 'personal' relationship with Jesus. It is, but it is so much more. My relationship with Jesus also involves the church I go to, the diocese I belong to, and the world-wide church I am a part of. This is why it bothers me when people say, "I can just pray at home, or by myself in the mountains - for I know God is there."
Yes, but you are missing the point! Yes, Jesus is there in the beauty of the mountains (or in the stream while you're fishing) - but He is also present in the Body of Christ assembled at your parish at Mass, in each one of the persons present! As much as you want to deny Jesus is there, because you know so-and-so is a drinker, and that person there is a gossiper, and she's an adulteress, and he's a cheat....
...that's exactly the point! Jesus is still there, in spite of all those peoples' sinfulness and in spite of my own. God is easy to see in the beauty of the mountains; and we can fool ourselves into thinking we are better than we are; but at Mass, with all of us sinners gathered, we are challenged to see in each other, despite all of our sinfulness, Jesus Christ. We are challenged to see God there. And so He calls to us to call Him not "My Father", but "Our Father" in heaven.