Barrel Proof is a proof that is in a barrel when taxes are assessed and it is to be bottled.
This number can vary widely from the Entry Proof due to aging conditions.
Aging in a hot environment and/or dry one can cause the proof to go up during aging, cold and/or wet environment (Think Scotland or France in Cognac) can cause it to go down.
In either case, a barrel proof bottling is the proof within 2 points of the assessed proof ( to allow for margin of error with equipment). In other words, nothing is added to the spirit during bottling to dilute it.