I'm so glad you asked this, because I've wondered what it meant too - but kept forgetting to look it up!
"Pushing the envelope" comes from the jargon of test pilots, and has actually been around since the end of the Second World War. The "envelope" involved is a sort of visual metaphor for the technical limits of a high-performance aircraft. A pilot who "pushes the envelope" and tries to exceed the known capabilities of the aircraft risks what engineers delicately term "catastrophic system failure," otherwise known as a crash.