A specific registered memory address within the Classic Mac OS. At the moment on my current machine it is located at 0x1950927C, but i'd imagine its exact value varies.

The area of memory immediately after the BowelsOfTheMemoryMgr address has enough funky stuff going on in it that a significant portion of all crashes are set off by problems in that particular block of memory. Thus, in an attempt to be helpful, the designers of the MacsBug tool set things up such that if MacsBug ever has to return a memory address in that area, it gives (and will accept when being given commands) the location of the address in relation to BowelsOfTheMemoryMgr in addition to the normal address. So, for example, upon being dropped into MacsBug following a crash you may see:
PowerPC unmapped memory exception at 195118AC BowelsOfTheMemoryMgr+08630
Which is certainly more a descriptive message, if not in most cases a more helpful one, than it would have been if the BowelsOfTheMemoryMgr address was not recognized by MacsBug.

In case you haven't guessed already, "Mgr" is short for "Manager".