The movie was made mostly as an experiment, rather than to tell a certain story and therefore has a strong arbitrary and surreal atmosphere. It features two men, Proog (the elder and more experienced) and Emo (the younger and more nervous) living in a miraculous construction referred to only as ‘the Machine’; Proog tries to introduce Emo to its nature but the latter is reluctant and argues about its purpose. The creators originally intended for the movie to show the abstraction of a computer.
The final message is not easy to see due to the abstract nature of the movie and therefore some viewers criticized it as pointless and random, and worthy of attention only if seen as a demo. Other people have widely different interpretations of its meaning. This slashdot comment for example describes the viewpoint that Proog represents the logical half of the brain, while Emo is the creative half. Proog cannot abide imaginative, unpredictable fun in his so carefully crafted and isolated logical world, which is why he tries to dominate Emo and eventually attacks him. Another theory is connected to the theory of evolution, with Proog and the Machine representing multicellular life and DNA, whereas Emo represents a single mitochondria and cannot grasp the complexity of the Machine.
Bassam Kurdali, Director of Elephants Dream, explained the plot of the movie by saying  :
“The story is very simple-I’m not sure you can call it a complete story even-It is about how people create ideas/stories/fictions/social realities and communicate them or impose them on others. Thus Proog has created (in his head) the concept of a special place/machine, that he tries to “show” to Emo. When Emo doesn’t accept his story, Proog becomes desperate and hits him. It’s a parable of human relationships really-You can substitute many ideas (money, religion, social institutions, property) instead of Proog’s machine-the story doesn’t say that creating ideas is bad, just hints that it is better to share ideas than force them on others. There are lots of little clues/hints about this in the movie-many little things have a meaning-but we’re not very “tight” with it, because we are hoping people will have their own ideas about the story, and make a new version of the movie. In this way (and others) we tie the story of the movie with the “open movie” idea.”
The title ‘Elephants Dream’ is also ambiguous. The original title was to be Machina but was dropped due to pronunciation issues. One motivation for the title regarding the story was the concept of an Elephant in the room, referring to the (unspoken) fact that Proog’s precious world only exists for him.