Everyone knows what a "right angle" is (90 degrees). A 45 degree angle is half that, or perfect diagonal. So yes we are talking angles of a triangle. The points of the Triangle are, the gun, the target, and the intersect straight above the target & the line of the barrel.
Well a minute of angle is 1/60 of 1 degree. So a 45 degree angle has 2700 minutes of angle. One minute of angle (MOA) just happens to be ~1.04" at 100 yards. Through "similar triangles" that doubles at 200 yards, triples at 300 yards & so on.
When you click your scope at 100 yards (when sighting in) you aren't turning it 1/4 of an inch left, right , up or down. It's a 1/4 MOA, it just happens to be very close to 1/4 of an inch...
1 degree = 60 minutes = 3600 seconds MOA is just used in "Rifle Lingo" because that is the scale in which scopes ore typically used. Mil-dots are radian & just the metric version like meters v/s feet.