Double has two speed ranges. High with 8 gears (assuming a 9 speed cassette), Low with 8 gears.

Triple has three speed ranges. High with 8 gears (assuming a 9 speed cassette), Middle with 9 gears, Low with 8 gears.

What you can use, stated above, is from Shimano and my real world use.

There is no need for a triple if you live, and only ride, in aflat area. Or are really strong.
On large hills and mountains, for most people, a triple covers everything.

Of course, everything goes out the window if the primary goal is to LOOK like a racer.