80×24 characters seems to be a very common default for terminal windows. This answer provides a very good historical reason as to why the width is 80 characters.
But why is the height commonly 24 (or 25) lines?
Terminal Standards – Why Is 24 Lines a Common Default Terminal Height?
coding-standardshistory
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You can thank the IBM punch card for this limit - it had 80 columns:
The reason the software uses those names is because the datasheets use those names. Since code at that level is very difficult to understand without the datasheet anyway, making variable names you can't search is extremely unhelpful.
That brings up the question of why datasheets use short names. That's probably because you often need to present the names in tables like this where you don't have room for 25-character identifiers:
Also, things like schematics, pin diagrams, and PCB silkscreens often are very cramped for space.
Best Answer
Early terminals were built around the same cathode ray tubes that were used for televisions. In the 1960's and 1970's these were all 4:3 aspect ratio.
If the display needs to fit 80 characters across the width then given the aspect ratio of the standard characters which was taller than 3:4 (if I remember correctly) and allowing for a larger space between lines than between characters you get to fit 24 or 25 lines on the display.
I haven't done the exact maths because I can't remember (or find) the exact character aspect ratio or line spacing.