(Or "snailmail", "smail" from "US Mail" via "USnail"; "paper mail"). Bits of dead tree sent via the postal service as opposed to electronic mail. One's postal address is, correspondingly, a "snail (mail) address". There have even been parody USnail posters and stamps made.
The variant "paper-net" is a hackish way of referring to the postal service, comparing it to a very slow, low-reliability network. Sig blocks sometimes include a "Paper-Net:" header just before the sender's postal address; common variants of this are "Papernet" and "P-Net". Note that the standard netiquette guidelines discourage this practice as a waste of bandwidth, since netters are quite unlikely to casually use postal addresses and if they really wanted your snail mail address they could always ask for it by e-mail.