It is a guide to keep the cleaning rod from chewing up the barrel, and keeps solvent from dripping into the action/trigger.
If you scroll about half way down, there is a discussion here:
Collecting and Shooting the Surplus Rifle - M-Pro 7 Report
That one is for cleaning bolt rifles from the breech end, there are also guides made for cleaning from the muzzle if the breech in is not accessible, like on an M1 Garand.