Alternative form of afternoon: the time of day from noon until early evening.
A gents' toilet room might be found in a house that caters for the cheaper class of theatrical patronage, where the slangy language of the "goin' to the mat this aft?" style prevails. A gents toilet room is not found in the Southern Hotel. It either "men's" or "gentlemen's".
AFT is an abbreviation for ana-fucking-tomic, frequently used by orthopedic surgery residents when describing an anatomic (or perfect) reduction of a fracture that they have reduced and fixed.
Ortho Resident 1: How'd that distal humerus fracture come out, are the post-op xrays back?
Ortho Resident 2: It took 6 hours but that thing is AFT - Ana-fucking-tomic