I am not an expert on the subject, but the purpose of lapping the bore is to remove tooling marks left from the rifling process, and ensure a dimensionally uniform bore from end to end. It provides a uniform, clean, polished interior finish that follows the direction of the rifling groove spiral.
The benefits of lapping are more consistency in velocity and accuracy, and eliminates much of the break-in process. It tends to gather less copper and fouling, which makes the barrel cleaning much easier, as well as reducing the difference in POI between clean and fouled barrels.
This is NOT a process for the novice, and if not done correctly, can result in barrel that will not give you the expected results, and will ruin accuracy.
It is completely useless in a custom competition barrel since they will come with this process already done. It is mostly done on barrels of the commercial grade, or barrels that have had damage due to bad cleaning techniques.
If you are thinking about having this done, it needs to be done by a PRO.
I lapped my Savage MLII when I first got it because my groups were about 4" apart out of the box, and it had lots of burrs down the barrel. After about 100 strokes, the barrel started shooting 1" groups consistently.
I could have probably done about the same thing by running 50 shots through the rifle, but the cost of powder and bullets, would have been quite expensive, and I got the rifle about 3 days before deer season, and I really did not have the time required to break in the rifle with this method.
By doing it this way, I was able to get the barrel done and sighted in properly with only two trips to the range, and it was good to go.