Re: remy 700 rail base
The MOA bases are taller in the back so they tilt the scope down and thus the barrel up. In the end, they move the range of adjustability for your scope so you can dial up more elevation. More elevation means that you can shoot longer ranges. The MOA number (10, 15, 20, or 40) is the amount of elevation change you get with that base.
As an example, my scope has 50MOA of adjustability which means 25 up and 25 down if everything is centered that allows me to shoot out to somewhere between 400 and 500 yards. With a 20MOA base added and everything zeroed, I end up with 5MOA down and 45 up which will get me out past 1000 yards. Just an example because it usually doesn't work out that neatly because of alignment issues, limited scope travel, etc but you get the idea.