Technically speaking, MOA stands for "Minute of Angle" - a measurement of angle equal to 1/60th of one degree. In practical terms, MOA refers to how much the scope base is tilted relative to the axis of the barrel. 0 MOA would be flat or parallel to the bore, while 20 MOA would tilt the scope down towards the barrel exactly 1/3 of a degree. (Doesn't sound like much, does it?)
Here is a graphic showing the path of a typical bullet out to 1,000 yards (red line):
The green wedge represents the possible area of adjustment of a typical scope mounted parallel to the barrel (0 MOA base). If you will notice, half of the possible adjustment area occurs well above the horizontal axis. This means that with a flat or 0 MOA base, you can only use about half of your scope's adjustment range. For most cartridges, this only starts to be a limitation out past 600 or 700 yards.
For shooters looking to use their scopes to the limit of their adjustments, a base that tilts the scope toward the barrel will trade upward adjustment for more usable downward adjustment. Here is an example of what a 20 MOA base would look like in the same scenario:
As you can see, the green wedge now extends out close to 1,000 yards, up from the roughly 800 yard limit imposed by using a 0 MOA base.
Now, before you go thinking "a little MOA is great, a lot must be better!", I suggest you take a look at the following example of the same scope using a 30 MOA base:
Yes, the maximum range is now extended to somewhere between 1,100 and 1,200 yards. But, and this is a big "but" - you won't be able to zero the scope at any distance less than 600 yards. This might be an acceptable trade-off for some long distance competition rifles, but most shooters would find this unacceptable.
As a general rule, keep the MOA of your base less than 1/2 of the vertical adjustment range of your scope. Any more than this, and you might not be able to zero the rifle at close range. Some older 1" tubed scopes might only have 30 or 40 MOA of total range, so you wouldn't want more than 15 or 20 MOA in that case. Most 30mm tubed scopes have adjustment ranges of 50-75 MOA, making a 20 MOA base a pretty safe bet.
If you have any questions, as always, we'd be happy to make a recommendation.