A music publisher is a company responsible for exploiting the copyrights of its songwriters and composers. This means pitching music to to potential licensees (artists, labels, TV/Film executives, etc.), taking care of all licenses and other paperwork on behalf of the songwriter, and ensuring they receive payment when their compositions are used. In return, they are entitled to a piece of the revenue generated.
If you haven’t signed a publishing deal, YOU ARE YOUR PUBLISHER! If you feel like you can’t take on the task of exploiting and administering your song catalog, then you should look into getting a publishing deal.