In creative businesses, a producer is almost the same kind of person as a director, but with different perspective to the outcome. Basically, a director has a strong artistic vision. A producer also may have artistic vision, but often less so. The main difference is this: The producer has the money, the director doesn't; The director looks at the production with the artistic desires in mind, the producer looks at the budget. The director has the art in mind, the producer does the boring things behind the scenes.
Let me tell you a heartwarming story about the realities of the movie making, OK? The producers say: "Make me a great movie with big explosions", and director says, "Okay, I got this great idea about a movie with big explosions and some love story too, get me actors, buy me stuff, get me a crew, and I'll get cameras a-rollin'". And the producer then arrange everything that doesn't touch that much the artistic thing, just the boring mundane things: Where to get staff, where to get actors, where (and especially when!) to get shit to blow up, and most of all, how the hell this all fits to the budget. And when the production starts, the producer then visits the set. He asks the director, "Have you made the scene with the big explosion?" and the director says, "Oh, yeah, we did that a couple of days ago, want to see it?" And the director then shows the scene from video, where the naked heroine gives the naked hero an apple, with the huuuuge explosion in the background beautifully symbolizing the great impact of the Original Sin. And the producer chuckles, saying to the director, "rest well, you all have done very good work."
(...okay, that was a stupid story, but I think it was enough for illustration.)
There are producers who pay very much attention to the creation itself, but there are also others just say "make me such-and such with something like blah and stuff there, and bring me the bill." The first type of producers also often leap to the director's seat, or otherwise participate in creation in their areas of expertise. The second type often also produce good dung.