I will pray something. Then I will go about my life and forget about it. One day that prayer will get answered in some way and I know because it's at that moment I remember that prayer! I have seen this play out in other's lives, too. Does the Spirit give us a sort of supernatural recall in that moment?
Something else is that being in a relationship with God is a partnership. He is partnering with us in prayer. We live out our lives interceeding for our loved ones or strangers or situations in prayer and we find peace. The more I pray the more I see God working. (He would have done the same things had I prayed or not because he is always at work), but when I pray I get to participate and see the results/blessings/gifts.
Prayer, to me, is going on an adventure!! It builds trust. It builds patience. It deepens faith. It has given me a refuge to run to whenever I have a need/concern/area that is beyond me. I am grateful for prayer and moreso for who is on the other side of those prayers!!