I used to call myself the "Curator of the Song" or "The Custodian" because a publisher takes care of your creation, from top to bottom. They will market, collect royalties, copyright and protect your song legally, so you can spend your time writing.
A publisher is someone you hire to take care of your business. They are a team in place, that is able to address most issues that may arise.
I was in the Creative Department at WarnerChappell, and was responsible for increasing revenue by selling the product and/or Songwriter. I was mostly called a "Songplugger" - someone who peddles songs to the artists that will record them. I would pitch songs to Faith Hill and if she cut a song then the writers got paid and the Publisher would take a percentage of that.
Beyond that a publisher will administrate 360 degrees, so you can actually make money!
A publisher can also be a big mouth-piece, promoting you to the industry, lifting you up to the peers you have always admired.
They are a partner, a sounding board and a good mirror for you. Most importantly, their responsibility is to represent you in the best light possible.