The process of making a movie requires a lot of input from a lot of different people. From grips and production assistants to cinematographers, screenwriters and directors, no one is completely responsible for the success (or unfortunate failure) of any film. Art direction is one of the many jobs that play a pivotal role in getting something from the written word to the flickering images you see in your local multiplex every weekend.
The term art director, is an overall title for a variety of similar job functions in advertising, publishing, film and television, the Internet, and video games.
Significance
Art direction is largely responsible for the visual look of a film. Generally an art department is in charge of things like designing costumes and sets and helping with lighting--generally helping with the appearance of everything that is in front of the camera. The art department also works with many other departments, like construction departments, to ensure everything goes smoothly after designs leave its hands.
Function
Art direction is a big part of what helps a movie achieve its identity. A movie that is forgettable in every way is obviously not likely to be one of a person's favorites. However, a great script, great production values and art direction can all keep them in your mind and help to make a movie a person wants to watch over and over again. Movies have a certain "look" and "feel" to them, which makes them visually interesting and therefore interesting in general to the viewer. That's not to say a movie with brilliant art direction can make up for a bad script, bad acting and horrid direction. It can't. But it can make for an extremely beautiful-looking bad movie.
Publishing
In publishing, where the term originated, an art director organizes the pages of a magazine or newspaper and in consultation with an editor, chooses or designs accompanying pictures or graphics.