I won't speak for all people, but for me Prayer has several meanings. I don't think you will like my answer, mainly b/c its hard to articulate a response to "why do people pray?" or "if everyone is praying, why is there so much bad in the world".
Spiritually speaking, accepting Jesus Christ as your Lord and Savior means entering in to a relationship. Not like one with my spouse or drinking buddies or anyone in this community, but a relationship deeper than anything we could touch or describe. I'm not a religions scholar and though I can describe in words many things, I find when I write about my Faith or Prayer or the Bible, I'm often at a loss for words. Ive always been reluctant to speak about my Faith with others, as I am far from perfect.
Prayer is a form of communication with God. He listens but the answers aren't always what we want, when or how we want them. We Pray because it's an outlet, its a form of dialogue; its a display of our appreciation for all the gifts and blessings we have a result of God sending his son to die on the cross for our sins. In the New Testament, we come to learn of a New Covenant with God. We thought we were getting a King with a sword, what we didn't have planned out is for a King (savior) who would wear a much different crown.
Prayer can be asking for forgiveness, giving thanks, requesting guidance....its a noun and a verb at the same time. I cant speak for your neighbor, but I presume she's Praying for you to come to peace with your decision to move. She likely values you as a neighbor and doesn't necessarily want you to leave , but alas you will make your own mind up about that. Her Praying you don't leave is, imo, her asking God to help her come to terms with whatever decision you make.
That probably a big nothing burger what i typed there, but on some level you may be wanting to be convinced of why prayer is a thing and I cant answer that for you. Only you can answer that. I cant sell you on the power of Prayer or why people do it....its not really a black and white topic easily answered, at least by this heathen. lol