Plain English Meaning
Patches of sky set aside for military pilots to practice maneuvers like aerobatics or formation flying. They have set boundaries, set heights, and set times when they are active. You can legally fly through one as a VFR pilot, but it is wise to check whether it is active and, if so, either avoid it or stay alert for fast military traffic.
Full Definition
Military Operation Areas are blocks of airspace established outside Class A airspace to separate certain non-hazardous military training activities — such as aerobatics, formation flying, and tactical maneuvering — from civilian IFR traffic. Each MOA has defined lateral boundaries, vertical limits, and active times, all published on aeronautical charts. VFR pilots are not from flying through an active MOA but should caution; IFR traffic is routed around an active MOA by , or it only when can be assured.