[kazinator]

The "monitor" term is not from early microcomputing but from early computing. I believe that "monitor" referring to a display monitor, and referring to a machine language debugger all have the same origin: they date back to directly monitoring the electrical signals from equipment to observe its workings. The use of "monitoring" in profiling (e.g. gprof and its gmon.out file, etc) is also the same.

[BLKNSLVR]

Similarly to 'monitor' speakers I would guess.

Something designed to keep track of a something-else that is running.

[kazinator]

Yes; mixing consoles have monitor buses. One way to use monitor speakers is to put them on the monitor bus output. Then any mixer channel that is bridged to the monitor bus (with a dedicated switch, like a push button toggle) is then monitored.