Morpheus has been searching for the One, a cyber-Christ who will destroy the Matrix and wake people out of their preprogrammed idea of life. Morpheus thinks he has found Him in Thomas Anderson (Keanu Reeves), who goes by "Neo" online. Morpheus and his fellow rebels (with equally stupid names: Trinity, Cypher, Switch, Apoc, Tank, and Mouse) enter the Matrix to find their Savior, but getting out is not that easy. You see, inside the Matrix are super-powerful agents bent on killing intruders, in much the same way that white blood cells attack a virus or disease.
The downside of returning to the Matrix after you've been awakened is that you can only escape it again if you can find an open phone line. The upside is that, while you're there, you can run and jump and fight like nobody's business. The fight scenes in The Matrix are awesome, perfectly capturing the style and energy of Asian martial arts and Hong Kong gun-shooting movies.
Personally, I come down in favor of the Matrix. I think that living a life complex enough to give the impression of free will is better than waking up in a dark, dank pod and scrounging around in an inhospitable future with guys named Apoc.
And as a critic, I come down in favor of The Matrix. Sure, the character names are stupid, the barroom metaphysics ("Hey, what if life is just a dream?") are simplistic, and the cyber-Christ story is predictable, but the action scenes--even the ones that use that 180 degree near-freeze frame--make this otherwise boring movie worth seeing.