So, you hear the term game producer a lot, and it's almost as popular as game designer. It's a term that's taken from film and television. More often in the game industry, it doesn't mean the same thing exactly. A game producer, to put it simply, is responsible for some aspect of delivering the game, and making sure that it's done right and on time.
Now, that title and the area of responsibility will very drastically be based on the company, the size of the project, the part of the world that you're in. You'll also hear terms that are similar to that, that might mean the same thing, like project manager or director of development, or development director. It just depends on the company, but really you should just know that as a producer, it's your job to make sure that the rest of team knows what they're doing, is delivering what they're supposed to be delivering, and doesn't have anything in their way to prevent them from doing that.