The term was coined in the realworld 1982 publication, The Imperial Fringe, and caught on after that being sporadically referred to throughout dozens of Trav publications over the years. The Imperial Fringe refers to the frontier of Imperial Space, society, and civilization. It's a ripe adventure playland and adventurers with the traveller gene often venture to or beyond it. Many of the early products, particularly adventure modules, refer to it by name, or by extended meaning terms such as outback or periphery. In fact, Imperial zones have a complicated sequence by which subsectors go from non-aligned to client state to frontier (district) to conventional Imperial Subsector. It is an established Imperial convention is to assign numbers to districts (for example, District 268) which are under Imperial protection pending integration into the Third Imperium.
The Fringe is in a sense, the Wild West of Traveller adventures, and the fringe subsector is the basic unit of adventure for Traveller RPG play.