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Coffin corner is the region of flight where a fast but subsonic fixed-wing aircraft's stall speed is near the critical Mach number, at a given gross weight and G-force loading. In this region of flight, it is very difficult to keep an airplane in stable flight. Because the stall speed is the minimum speed required to maintain level flight, any reduction in speed will cause the airplane to stall and lose altitude. Because the critical Mach number is the maximum speed at which air can travel over the wings without losing lift due to flow separation and shock waves, any increase in speed will cause the airplane to lose lift, or to pitch heavily nose-down, and lose altitude.
The "corner" refers to the triangular shape at the top of a flight envelope chart where the stall speed and critical Mach number are within a few knots of each other. The "coffin" refers to the possible death in these kinds of stalls. The speed where they meet is the ceiling of the aircraft. This is distinct from the same term used for helicopters when outside the auto-rotation envelope as seen in the height-velocity diagram.