Spoiler warning: Plot details follow.
Computer programmer Thomas Anderson leads a secret life as a hacker under the alias "Neo". Neo meets a mysterious figure named Morpheus who offers him a chance to learn the truth about his world, which Neo accepts.
Neo learns that rather than living in the year 1999 as he believed, he is actually in approximately 2199. Neo has spent his entire life living in an elaborate simulated reality maintained by intelligent computers to keep humans under control. Most of humanity lives in cryogenic pods, where they are fed intravenously and the computer feeds them false input about the world.
The subject of an illusory world has been explored as far back as 1641, when René Descartes speculated in his Meditations on First Philosophy that the world might be an illusion created by an evil demon. Ultimately Descartes rejected the idea that this could possibly be true, but in order to do this he had to invoke the idea of a good God who would not allow this to happen. This line of reasoning is not open to atheists.
Indeed, it seems that there is no way to conclusively prove that the world is not an illusion, if we are allowed to make the assumption that such an illusion would be so skillfully made that it was indistinguishable from reality. Science is only able to state facts about the world with a limited degree of certainty. While scientists may deem one hypothesis as more likely to be true than another, any explanation which fit the available facts must be considered "possibly true", although subject to conditional dismissal based on Occam's Razor.
If we cannot even assert conclusively that the real world exists, then it is fair to say that we can never truly "know" whether something like a god exists. Therefore, the Matrix is sometimes brought up as a way of illustrating why weak atheism makes more sense than strong atheism.