According to the dictionary, to publish something means to make it publicly available. Therefore, a music publisher would be one who makes music publicly available. In reality, though, in the music business, a publisher’s real role (typically) is to exploit musical works commercially. Once a songwriter creates a song and affixes it in a tangible medium (such as by writing it down, or recording it on tape) the writer owns the copyright in that piece of intellectual property. However, that copyright isn’t worth very much in terms of dollars and cents unless there is some mechanism by which to create a demand for the right to copy that intellectual property (the song). Demand is created when someone other than the author wants to do something with the song. If an artist (such as a rock performer) wants to record that song on their next album, the copyright owner can charge the person who wants to use their song. This is usually done by issuing a license to allow them to record the song and distribute copies in exchange for a fee. There are many uses for songs such as background music, printed sheet music, soundtracks in movies, songbooks, etc.
The role of the publisher is to seek out, secure, and handle the logistics of commercially exploiting a song. Usually, the songwriter assigns the copyright to the publisher, and the writer and publisher share in the amounts received. If a songwriter has the connections, business savvy, time, and wherewithall to fulfill these functions on their own, they have no need for a publisher (they act as their own publisher) and thus don’t need to share their profits with a publisher. If a songwriter cannot, or does not wish to handle these tasks, they will often work with a music publisher. It is important to find a publisher who believes in your work, and has the connections required to procure commercial uses for your music. If the publisher has no better connections than you do, it is not that likely that he or she will be able to do much more with your music than you can. Sometimes publishers are connected into specific areas, and can thus help your songs get noticed in certain arenas.
Another function of a publisher is to register your songs with the appropriate Performing Rights Organization (PRO). In the United States the three PROs are ASCAP, BMI, and SESAC. As a writer you should affiliate with one of these groups. You then work with a publisher who is also affiliated with the same group. Often a publisher will actually have more than one publishing company, where each one is affiliated with a different PRO (so they can work with writers from more than one PRO). The PROs collect money from venues that use music (such as nightclubs, radio, television, etc.) and pay money to songwriters and publishers based on how many times their songs appear in the PROs surveys. (Check out each of the PROs to learn how they conduct surveys, and the formulas by which they pay royalties)
Some publisihers (such as Zimbalon Publishing) who publish works likely to be performed in church are also affiliated with Christian Copyright Licensing International (CCLI). CCLI aids churches in responsibly using copyrighted material, and provides a mechanism for songwriters to be paid for church uses.
Hopefully this short blurb has helped you to understand a little bit of what a music publisher is, and what they do.