I began producing theater after getting my MFA in acting from the Actors Studio in 2004.
Of course, I had no idea the breadth of tasks and skills that producing entails... I just knew I wanted to make my own opportunities.
I produced 2 plays with a friend from grad school and then hung up my own proverbial shingle with Tongue in Cheek Theater Productions in 2006. I've been producing thought-provoking comedies ever since.
32 productions later and counting... the short answer to "What is a producer?" is... a person willing to do everything that needs doing.
Yet that makes it sound like a chore, and it isn't (at least for me!). I love to make lists of things that need doing and then ticking each off as I go: obtaining the rights, submitting paperwork to Actors Equity, hiring cast and crew, audition sides, costume measurements, design meetings, ordering props and furniture, and... rehearsals, and bookkeeping, and promoting the show. The list is long but I love the variety and getting to work with other people who pour their talents into it, too.
So I guess a better answer to this question is, "a lot of fun."