a nonprofit general store at a military base, for the sale of merchandise for personal use, refreshments, etc.
See Base Exchange in American Heritage Dictionary 4
Abbr. BX
A service mark used for general merchandise store services for government employees on a naval or air force base. This service mark, often lowercased, sometimes occurs in print with the meaning “a general merchandise store on a military base”: “The products are distributed at Army and Air Force base exchanges”(Washington Post).