This is a superscription that tells about the psalm. Some scholars say that this is part of the scripture and some say that it is not. (See "What are Superscriptions in Psalms" in [Introduction to Psalms](../front/intro.md).)
The words "my prayer" are a metonym for the person who is praying. See how these words are translated in [Psalms 39:12](../039/012.md). Alternate translation: "Listen to me as I pray to you" or "Be willing to do what I ask you to do" (See: [[rc://en/ta/man/jit/figs-metonymy]])