80x24 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?
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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.
The height of the vt100 terminal.
Emulators get the best vt100 compatability at that size.