The offset insert kit allows the following:
Gain more elevation than your scope has available. This was the problem I had. Scope maxed out on elevation and still 6" low at 50 yards. Not good. I had another scope on there and it could be adjusted high enough, but was not a very good scope. Some scopes just don't have as much vertical elevation as you need, and even slight misalignments in the vertical or horizontal mounting of the rings really adds up.
If you center your scope adjustments, the scope should have the best optical characteristics. By using offset rings (and boresighter) you can make most of the sighting adjustments before you leave for the range. Then it's just a few clicks to fine tune the scope. You'll be looking very close to the center of the lenses, and I noticed a difference.
This offset kit is better than shimming because it applies even pressure and gripping power around the entire scope ring circumference. This prevents scope binding and possible internal damage from slightly misaligned rings. The inserts are a hard plastic, that also protect the scope finish from scratching under the rings. I'm sure you've seen a scope that had scratched paint around where the rings were attached.
The Burris rings are the only ones that have the insert kit (that I found), are all steel, have Torx screws (way better than Allen in my opinion, as the don't seem to strip as easily), and are made in the USA. I was sceptical but hopeful that these things could solve my problem, and was getting frustrated enough to sell the gun. After sighting it in in about 15 minutes after using the kit and boresighter, I was sold. Every set of rings from here on out will be the Burris for me. Sorry to sound like a shill for Burris, but I am really happy with the product.