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It is a function of measuring scope adjustment.
It is a mathmatical term used to measure degrees.

In the rifle world, it's used to measure groups, or elevation/windage doping.
 
1 MOA = 1 minute of angle,

which is 1/60 of 1 degree, which works out to pretty darn close to 1" at 100yds.

When refering to a rifle, it is generally refering to the accuracy capability of the rifle - ie, what it will do under near perfect conditions. (How tight it will group, eg a 1 moa rifle will keep all shots of a group within 1" of each other.)

In reference to a scope, it's generally either reference to the size of the reticle or to the amount of adjustment a "click" of the turret moves the reticle. Many/most scopes use 1/4 moa adjusters, which means each click moves your point of aim about 1/4" at 100yds. A red dot with a 3 moa dot will have a dot that covers a 3" circle viewed at 100 yards.

It's basically a convenient measuring system that's easy to calculate in your head.
 

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