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?
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.