Scope ring lapping is when you grind off any uneven surfaces on the inside of scope rings. This means there is much less chance of your scope getting scraped or dented as well as allowing more of the ring surface to come into contact with the scope, allowing less movement.
A scope lapping device
From Michael Carlin (via TheFiringLine forum)
Lapping scope rings trues the rings to each other. The new rings may have been well machined, but when mounted on various (note the intent to imply differences) recievers of the same make they may not be perfectly aligned with each other.
This was one of the reasons that when I was young the one piece base was supposedly superior. It tended to limit the amount of misalignment that the gunsmith could induce in installing two piece base systems.
So what you ask?
This is very important, for if the tube is tweaked, kinked, or otherwise stressed, the internal adjustments will be “bound up” by the stresses. Imagine what would happen to any precision instrument that was twisted about its long axis. The amount of bind will adversely affect the repeatability of adjustment.
The best scopes in the world will not perform to their potential if their mount torques the tube, and binds up their internals.
Additionally, stresses applied to the tube tend to degrade the optical performance. Optimum optical performance requires that the optical centers of the elements (lens) be aligned. This is definitely not going to be true if we twist the scope out of shape squeezing it into misaligned rings.
Those of you who mount a scope on your 2+ minute of angle rifle to shoot deer at 100 yards, never “sight in” at any other range, and have not touched the adjustments of your scope for years may find all of this very boringly esoteric.
Those of you shooting any rifle any sight matches at 800, 900 and 1000 yards, as well as the silhouette shooters, and long range varminters/benchresters may consider this much more important.
Is lapping necessary? It depends. If your are installing a $40 scope on a $275 factory rifle to shoot factory loads at a large game animal at under 200 yards… probably not.
If you installing a $500 instrument on a rifle capable of using that level of precision due to its accuracy, it definitely is IMHO worth the limited expense and effort to do so.
Guns Magazine wrote a review of the Brownells scope ring lapper.
I found a very good scope lapping tutorial here.