Max Q is NASA talk for 'maximum dynamic pressure.' It is used to describe the point during a spacecraft launch and ascent at which it experiences the maximum pressure on its structure due to atmospheric drag. If the vehicle maintains a steady acceleration, this is reached fairly rapidly, since the earth's atmosphere drops off in density quite rapidly at altitude.

This phrase is heard during coverage of Space Shuttle launches, and presages clearance for the orbiter to increase SSME thrust back to maximum. The engines are throttled down shortly after launch to keep Q low so as to not damage the shuttle; then, after max Q is reached, the clearance 'Go for throttle-up' will usually be given by ground control.