In the context of determining the meaning of a discovered URI, "Follow Your Nose" is an informal way to say FollowLinksForMoreInformation.
In the context of messaging, "Follow Your Nose" is about walking through a message, outside-in, and interpreting semantics via the successive application of unambiguously associated specifications (public ones, and registries, in the case of the Web). (See how DanConnolly first(?) used the term.)
In either case, the recipient is following a well-defined process for locating the information needed to figure out how to interpret the URI or message.
An important part of this process is DereferenceURI.
See also, Specs Count by Tim Berners-Lee