A handkerchief or tissue. Implicit in the word is that the handkerchief or tissue has been used and that the product within it is particularly vile, greasy, and slimy; the result of diseased sinuses or a severe nasal infection. By extension the word can be used to describe a person having the same qualities, an obnoxious, slimeball whose very presence makes people nauseous.
Gordon's tried to cop off with Alice again.
Fuckin' snotrag needs a good smack in the chops.
Handkerchief, a piece of cloth kept in the back pockets of toothless rednecks, that when pulled out and "waved about" serves as a signal that they're about to sneeze or hack up a lung in a particularly disgusting manner.
Cousin Billy-Bob, kin I borry your snotrag? I gots ta' aaah-AAACHOOOO!! Sorry 'bout that cousin Billy-Bob......club soda'll take that right out.