Promoters do just what their name suggests - they promoter live shows. But more than just promoting the show, promoters also organize shows and book bands. The basic duties of a promoter are to secure a venue for a show, promote the show via the media and via posters/flyers/etc in the local area, work with the band and agent to make sure all the show night needs are covered (PA system, lighting, etc), and when appropriate, promoters pay the band. The promoter is responsible for covering the venue costs and the costs of promotion and any special equipment. However, promoters can, and do, recoup these costs from the show income before they pay the band in many instances. Every deal is different, and promoters work with agents and managers to nail down the specifics of a deal before the show.
Some promoters, especially indie music promoters, put on shows for the love of it and actually end up spending more than they make. If you do make a deal with a promoter for profits from the show, you will likely have either a set amount that you will be paid, no matter how many people turn up, or a "door split" agreement, wherein the band and the promoter will split the proceeds from the show on a percentage basis, after the promoter has recouped his/her costs. Door splits can be 50/50, but often they are 70/30 or 80/20, in favor of the band.