Cleaning Patch
A cloth square pushed through the bore on a jag to apply solvent and wipe loosened carbon and copper back out of the barrel.
A cleaning patch is a small square or round piece of cotton flannel, sized to caliber, that does the wiping in a cleaning routine. Speared or wrapped onto a jag and driven through on a cleaning-rod, a wet patch lays down bore-solvent and a dry patch carries the dissolved residue out the muzzle. The patch needs to fit snugly enough to contact the rifling without being so tight that the rod bows.
Patches are the diagnostic step as much as the cleaning step. Shooters read each one as it comes out: heavy color means solvent is still lifting fouling, and patches coming out clean and dry signal the bore is close to done. They are single-use and cheap, so most people run a fresh patch on every pass rather than reusing a dirty one and redepositing grit.