Plain English Meaning
An area of sky set aside for military training like aerobatics, formation flying, or air combat practice. Civilian aircraft can fly through it, but they should be very careful when it's active because military jets may be maneuvering aggressively.
Full Definition
A block of airspace with defined vertical and lateral limits, established outside Class A airspace, used to separate certain military training activities from IFR traffic. VFR aircraft are not prohibited from entering an active MOA but are strongly advised to exercise extreme caution. IFR traffic may be cleared through an active MOA only if ATC can provide separation from the military activity; otherwise, will be routed around it.