Minute Of Angle.
It's a measure of an angle that's 1/60th of a degree.
Angles can be measured in Degree's, Minutes, and Seconds.
There's 360 degree's in a circle, 60 minutes in a degree, and 60 seconds in a minute.
At 100 yards, a minute (or moa) covers a circle approximately 1.047197 inches in diameter. At 200 yards it covers 2.094395 inches...at 400 yards its 4.188779.... at 1000 yards its 10.47 inches... at 2000 yards its 20.94 inches
Most people just use 1" for every 100 yards.
It's often used to describe how accurate you and/or your gun can consistently shoot.
If you get a 1/2" group at 100 yards, you are shooting a 1/2 MOA.
A 5" group at 500 yards is 1 MOA.
A 10" group at 1000 yards is 1 MOA
A 2.5" group at 1000 yards is 1/4 MOA.
It can also be used to give "hold over" corrections for shooting long range for a given trajectory. For example at 600 yards, at 4500ft elevation, 59 degrees, with a muzzle velocity of 3100 ft/sec, a 150 grain bullet, with a .277" diameter and a BC (ballistic coefficient) of .525, I have a drop of 10 MOA. (I got this using a ballistics calculator) If I'm using a nightforce scope with a np-r1 reticle.... since each vertical tick is 1 MOA, I just hold over 10 ticks from center and shoot.
Instead of holding over, since there is 4 clicks per minute, I could have dialed 40 clicks up. Then held right on.
Hope this helped.