I vaguely remember asking my mom about this when I was younger. Mom was the religious leader of our family, and I considered her a good authority on the subject because she said she almost lost her faith in college and did her own research which led her back to God.
She told me the act of prayer itself was a form of praise, an exercise of humility and deference to God. It doesn't mean that God will change his mind; it just shows you're humbling yourself before him and submitting to his will.
It hardly makes sense to me now but I bought into it 100% at the time.