I'm not sure why what we do is so mysterious. It's pretty obvious to me that someone had to organize and make sure a film is managed appropriately. There had to be that key person or two who championed the project to the world of talent, financiers, agents, managers, distributors, festivals, etc. And kept the show going through the ups and downs of development, pre-production, production, post production and distribution.
A film is a small business. Limited Liability Companies are formed and the producer is usually the Managing Member. We can be likened to the CEOs, CFOs, and Presidents of companies. All decisions (right or wrong) are made or approved by us. If the project needs something, we are in charge of finding it. Any problems? We fix them. We are the Captains of the ships, working to keep everything afloat.
There's a reason why producers win Best Picture. They are accountable for the success of their pictures -- good or bad. Sure, the writer and director do share the responsibility for the picture's success but in the end, the producer is the one helming the project. He or she could have developed the story a little more with the writer or worked with the director on his or her weaknesses.
So the next time you see a good film, congratulate the writer and director and throw a few snaps in the direction of the producer. He or she worked hard to entertain you.