A circle of powder, ringing the inside of one's nostril which can be left over (or I suppose even BUILD UP) from the ingestion of an illegal drug in powder form by "snorting", or quickly inhaling said powder through a small straw or glass tube (usually known as a "Tooter")inserted directly into a nostril. Most common among cocaine users; however, the term "felony ring" was first coined by meth-amphetamine users, since if the wrong person noticed, it could lead to a felony charge, as the laws are quite strict and harsh for what could be considered MINISCULE amounts of the drug. In essence, a felony ring contains enough of the drug, in weight, for one to be charged with a felony.
(In the same sense as two friends who are running a few quick checks on each other's appearance before going into a packed night club)
"Any felony rings? No? Good- no jail for ME today!"