Every song has two parts to it: the recording side and the composition side.
Master recordings refer to the recording of a musical performance that can be played back, or reproduced.
You can make money off of master recordings by selling your own recordings directly to your audience (for example, make your own CDs and sell them at your shows, or use an online aggregator like Too Lost, to distribute your master recordings to platforms like iTunes, Spotify or Apple Music.)
The underlying composition - also referred to as the music publishing - is the underlying musical composition of a piece of music; the music and lyrics.
Music publishing refers to the money you make from government mandated royalties that must be paid to you when other people or companies use music that you wrote (the composition). That can refer to your record company making a copy of your music (mechanical royalties), when a radio station, website, or restaurant plays your music to help them make money (public performance royalties), or if a television show or film uses your music in their productions (sync royalties).