If you think of a film as a building site, the director is the foreman and the producer is the developer.
The director will generally be in charge of eliciting the best performance from the cast and framing the shots/deciding on the angles etc and will also be involved in the post-production editing. S/he will, in general, be in charge of the "artistic" side of things.
The producer will be more of a "money" person, but as such probably has a bigger say in what goes on; though is not likely to be as "hands on" as the director.
Better definitions:
http://www.imdb.com/Glossary/
Various rules apply, but you often see lots of "co-" or "executive" producers. As well as the IMDB definitions, sometimes (particularly in TV) these are honorifics with a lesser degree of power designed to keep actors (in particular) sweet. I've noticed that in Season 3 of "Bones" both the two leads are now exec producers.