Holy cow, I wrote a book!
The double-click time is sort of the dialog unit of time. It's used as the basis for many user interface time values that don't have their own custom setting. Here are just a few examples, along with the values you get if you leave the double-click time at its default of 500ms:
SPI_SETMENUSHOWDELAY
If you go into the mouse control panel and speed up your double-click speed, then you'll find that other user interface operations tend to speed up as well. The double-click time is a sort of barometer for how good the user's reaction time is. If you set it too low, you may find that things just happen too fast.