Can someone explain what a "standard time signature" is, in terms of frequency, for someone who has no clue whatsoever about music theory? As far as I understand it, there's a duration which loops (e.g. 0.5 sec for 120 bpm) and then you subdivide that into something (I guess).

How can this not be an exact measure of a time signature, since you can pick an arbitrary amount of time, loop it and subdivide it into parts?

There are a number of different subdivisions. First there is the bars, that you could define as a complete cycle. Inside the bars there are beats, often 2 or 3 per bar, most often 4. Then each beat is divided in 2 or 3 parts.

Then you can play it slower or faster, that's the tempo.

Notice that it's just about the rythm of a song. The actual notes you can place on it wherever you feel. Of course you want them to match some subdivision for them to feel "right" but often intentionally shifted for expressivity (swing).

Some standard signatures are:

4/4 - Bars of 4 beats naturally divided in two (most songs)

3/4 - Bars of 3 beats naturally divided in two (waltz)

2/4 - Bars of 2 beats naturally divided in two (march)

12/8 - Bars of 4 beats naturally divided in three (used in blues)

The /4 or /8 difference is moot. It's the duration of the beat, but you can compensate it with tempo.

That helps, thank you! Given that bars contain beats, why is the Terminator theme such a mystery? Doesn't it also have bars that contain beats? Or is the problem that the beats are so irregular that they aren't spaced somewhat evenly in the bar?

The term "standard time signature" isn't a technical term. I just meant it to refer to time signatures with relatively low integers, as opposed to something crazy like 101/32.