When movies.stackexchange.com was announced, the very first thing I thought of was "how long after launch before someone asks for an analysis of 'Mulholland Drive'?"
Having said that, here is the very abridged version of what's going on.
The viewer knows a couple of key points:
- Rita gets into a car accident and suffers amnesia.
- She meets Diane who is trying to become a Hollywood actress.
- Mysterious things start to happen and Diane is interested in helping Rita explore/solve those mysteries.
As is typical in Lynch fashion, things begin to become unclear quickly, and there is a definitive point in the movie where things switch around.
When the box is opened, the perspective changes. Although the viewer may not realize it, he is now in the real world, the waking world of Diane/Betty. The entire first part of the film, up to the opening of the box, has been in Diane/Betty's dream. Betty has ultimately come into contact with all of the various people (in real life) that she has seen in her dream, and (as is typical with our dreams) faces / events are re-arranged, mixed up, and re-associated to form bizarre stories.
The opening of the box symbolizes Diane/Betty waking up.
The order of events are re-arranged so thethat we, the viewer, are able to piece together the puzzle (ie. Betty coming into contact with a person in real-life...who then becomes a face --but an entirely different person with different motives--in her dream).
A much more thorough analysis can be found here.