Sniffing is the ability to "smell" where violence has occurred. The strength of the smell depends on the severity of the violence; the smell of a murder will last much longer than the smell of a petty robbery. Sniffing is a very rare ability. Many rulers have sniffers, though they keep them secret.
In The Great Hunt, Hurin is a sniffer who is enlisted by Ingtar to help track Padan Fain and the Darkfriends and Trollocs who have taken the Horn of Valere. During their trek many find that Perrin has a similar sense of smell so to keep his cover he says he is an apprentice to Hurin.