The phrase "push the envelope" means to go beyond the limits of what is considered possible or acceptable, often by innovating or taking risks. 

The origin of this phrase is closely tied to the field of aviation, particularly in the context of test pilots and their daring flights. 

When a test pilot "pushes the envelope," they are testing the aircraft's capabilities at or beyond its known limits. The term "envelope" in a mathematical and engineering context refers to a curve or boundary that encompasses other curves or data points. In aviation, this idea translates to the flight envelope, which encompasses the safe operating parameters of an aircraft. 

The flight envelope refers to the operational limits of an aircraft, including its speed, altitude, and maneuverability. It defines the boundaries within which the aircraft can safely operate. Test pilots are often tasked with exploring these limits, testing the aircraft's performance under extreme conditions to ensure safety and reliability. 

The phrase "push the envelope" was popularized by Tom Wolfe's 1979 book "The Right Stuff," which chronicles the lives and careers of test pilots and astronauts. Wolfe used the phrase to describe the daring and risk-taking nature of these individuals as they tested the boundaries of aviation technology and human endurance.