Plain English Meaning
Cars and boats move across a flat surface. Aircraft also move up and down. That up-and-down movement is what pilots mean by 'the third dimension.'
Full Definition
In aviation, the third dimension refers to vertical movement through the atmosphere — the ability of an aircraft to climb, descend, and operate at varying altitudes — in addition to the two horizontal dimensions of forward/back and left/right movement that ground vehicles are limited to.
Context Anchor
Seen in aerodynamics discussions when the handbook moves from basic airfoil lift to what happens on an actual airplane .