Pushing the envelope.
To attempt to extend the current limits of performance; to go beyond commonloy accepted boundaries.
The envelope referred to is not the receptacle for sending letters but an area enclosed or enveloped.
In this way it has a lot in common with the phrase “beyond the pale”. This phrase refers not to a light colour, as in Procol Harum’s Whiter Shade of Pale, but to a stake or pointed piece of wood. It is virtually obsolete now except in the phrase “beyond the pale” and in the associated words paling (as in paling fence) and impale (as in Dracula movies). Pale came to mean an area enclosed by a paling fence, a safe area, so that “beyond the pale” came to mean leaving the safety of home. Inside the pale you were safe, outside the pale you were at risk, giving rise to the current meaning of unacceptable, outside agreed standards of decency.
The envelope was much the same as the pale. The term "pushing the envelope" had been in use since World War 2 in flight and aeronautic fields. The “flight envelope” as it was known, was a description for the upper and lower limits of safe flight, taking into account such factors as speed, engine power, manoeuvrability, wind speed, altitude etc. By 'pushing the envelope', i.e. testing those limits, test pilots were able to determine just how far it was safe to go.
In 1979 Tom Wolfe used the phrase in his book about the space programme, The Right Stuff:
"One of the phrases that kept running through the conversation was ‘pushing the outside of the envelope’... [That] seemed to be the great challenge and satisfaction of flight test."
That use popularised the term, taking it from flight and aeronautical fields into general usage.