Rabbi Akiva used to begin some of his prayers by saying, “Avinu, Malkeynu.”
It means, “Our Father, Our King.”
What’s the difference between them?
A king has absolute power. He (or she, if a queen) can make autocratic decisions with little regard for the consequences on his subjects. The subjects have little or no recourse. A king often can’t even countermand his own edicts (see “Esther”), if he changes his mind after declaring them. It’s a “distant” relationship, in a personal sense.
A father, however, (ideally) does everything with his children’s best interests at heart. While he might, like a king, have absolute power, his use of that power is always tempered by what he knows to be best for the children. It’s an intimate relationship personally.
For Rabbi Akiva to address G-d as both — at the same time — is to say (in prayer), “G-d, my connection with you is based on totally accepting Your Authority, while, at the same time, recognizing your endless Caring for me.”
In another sense, though, calling G-d “King” implies a recognition of G-d’s control of all things. If this doesn’t immediately lead to an experience of G-d’s Presence, it must ultimately do so. G-d’s control over all things is based on G-d’s Presence in all things. G-d isn’t a “puppeteer,” moving things from afar (even though the puppet’s strings are themselves “connections” between the puppet and the puppeteer). G-d “moves” things by being part of them.
I’d even say that the mere two words “Avinu Malkeynu” can be themselves a kind of prayer, if by saying them, they affirm in our awareness G-d’s unchanging Presence and Goodness.
“Petitionary prayer” — the kind of prayer where you ask G-d for things (there are other kinds of prayer, too) — can begin with a request. But people who pray regularly find that they need time to turn their mind from the problem to G-d. The invocation “Avinu Malkeynu” can then help make that transition as you begin praying.
But it’s also true that once you’ve made the request, you want to turn your attention (again) from your needs to G-d’s Presence. In that case, the words “Avinu Malkeynu” serve as a final step in prayer. Turning our attention to G-d, our prayer becomes a contemplation. G-d’s Presence is blissful (or “Bliss” itself), whether or not our requests are responded to positively or not.
In fact, after experiencing G-d’s Presence in prayer, the outcome can matter a lot less.
Your request is part of your lower self. G-d’s Presence is part of your Higher Self.
The joy and peace of G-d’s Presence, which is given to us freely and always with us, is a better result than anything we could ask for.