The term “Moly” refers to Molybdenum Disulphide. This is an extremely fine powder which acts as an inert lubricant between the bullet and the bore. It is coated onto bullets to reduce the friction incurred on the bullet as it passes down the bore. The reduced friction is said to prolong barrel life, increase velocity and the ballistic coefficient, and increase accuracy. The moly coating does not build up in the barrel, as each successive shot removes any excess material from the previous round.
If you are worried about barrel break-in on new rifles, do not use moly to begin with. The extra friction from an uncoated bullet is necessary for proper break-in.