It makes us feel better... that is it. It does not help in any other way because there is no God and even if there was he does not answer any prayers.
Prayer is simply communicating with God and being closer to his presence as a result.
Prayer is not just simply asking for things. It involves acknowleging God as Lord, praise, confession, praying for others, praying for ourselves, asking for guidance, and simply 'being' in the presence of God. And, of course, listening for God speaking to us through his Holy Spirit.
Therefore prayer helps us draw closer to God by 2-way communication, and, as a result of growing nearer to
him, we grow spiritually ourselves.