This is a question that can be explained in a few sentences, or in a 5,000-word-long essay. Let’s start with the former.
Music publishing is, essentially, the management of music copyrights in any commercial manner. The entire field is based on taking creative works, in this case, songs, and finding ways to use them commercially. It is also about ensuring that when songs are used in some way and money is owed, it’s properly accounted for, collected, and dispensed to copyright owners in a timely manner.
The definition makes it seem fairly simple, and at its heart, music publishing is easy to understand. It’s one person writing a song, and another using it in a movie, playing it at a bar, or streaming it on Spotify. Then, a company tracks all that usage, collects the money owed for using that tune, and pays the creator.
Diving into the subject is when it quickly becomes a bit more confusing, but it can all be understood with a bit of time and patience.