Minute of angle
In easy terms, Minute Of Angle is a measure of accuracy which basically means 1" @ 100 yd, 2" @ 200 yd, 3" @300 yd and so on.
Mathematically... Imagine you are standing in the center of a circle that is 200 yards across. You are 100 yards from edge of the circle and are shooting at a target at teh edge. The diameter of the circle is then 7200" and the circumference is pi* the diameter, or 22619.4671". 22620" for simplicity's sake. The circle has 360 degrees around its circumference, so 1 degree is 22620/360 , or 62.83". a minute is 1/60 of a degree, so 1 minute of angle at 100 yd would equal 1/60*62.83", or 1.047"
If you do this math on a circle of 200, 300,... yards, you'll see that it roughly equates to an inch per 100 yards.
So if someone tells you they're shooting sub MOA groups, they're shooting <1" groups at 100 yards, <2'" at 200 yd, <3" at 300, and so on. If a scope features 1/4" MOA adjustments, one click will mive your group 1/4" at 100 yd, 3/4" at 300 yd, and coming back in the other way, 1/8" at 50 yd.