You are right. If your scope has 1/4 inch "clicks", it will take 4 clicks to change the point of impact 1 inch at 100 yards, but only 2 clicks to make a 1 inch change at 200, and 1 click will make a 1 inch change at 400 yards.
All scopes do not have 1/4 inch adjustments. I have an older Luepold that has 1/2 inch clicks, so be sure you know what you have. Usually this is indicated inside your scope turret covers or on the ring around the adjustment screws. If you can't find it, you can always call the scope manufacturer and ask them. (They'll want to know the model number.)
As for minute of angle itself, I believe it is established more or less like a compass with 360 degrees making up the complete circle. So, if you are looking straight out at your target at 100 yards, a one degree (4 clicks) move, up or down would measure 1 inch at that range. Theoretically, if you could "click" your scope up 360 times that would be 90 degrees and your bullet would be shooting straight up.
Good shooting and good hunting!