VFG are the German felt-cleaning system — a shaped felt plug that goes through the bore on a pull-through or an adapter instead of a patch on a jag.
Why felts rather than a rod
The felt is a light interference fit, so it sweeps the bore without a steel rod anywhere near the crown. Crown damage from a carelessly used rod is one of the quickest ways to lose accuracy on an otherwise sound barrel, and it is the reason a lot of target shooters will not put a rod down a muzzle at all. A pull-through kit that lives in a pocket also gets used, which a bench rod at home does not.
Plain and drilled
Plain felts do the dry pass. The drilled felts — the 610 in .22 and the .177 Match-Set felts — take a drop of solvent or oil through the hole so it works from the middle out rather than being wiped off on the first inch of rifling. Run a solvent felt, let it sit, then follow with plain felts until they come out clean.
The kits
The Firearm Pocket Set Cal.22 and the .177 Match-Set Pocket are the complete pull-through kits. Boxes of replacement felts in .177 (100) and .22 (80) are listed separately.
See also: Cleaning Kits · Airgun Accessories · Gunstock Care