Plain English Meaning
Ground that rises and falls sharply enough to be officially classified as mountains for flight planning. The FAA has drawn lines on the map showing exactly which regions count, and inside those regions pilots must keep extra altitude above the ground.
Full Definition
An area of terrain where the elevation changes by more than 3,000 feet within a horizontal distance of 10 nautical miles. Designated mountainous areas in the United States are listed in 14 CFR Part 95 and are depicted on FAA charts. Operations in mountainous terrain require higher obstacle clearance margins on instrument procedures (typically 2,000 feet above the highest obstacle within the protected area, versus 1,000 feet in non-mountainous areas).