How big is a story?

You mean like measurements? Or what? A four story building is a building with 4 floors(levels) in it. Get on the elevator and go to the 4th floor, that's as far as it goes. Is that what you mean?

A story is roughly 10 feet tall

A story is a floor, so it depends on the ceiling height of each of the floors. It probably is around 10 feet.

The building I worked in was constructed in 2006. The space from the floor to the drop ceiling was 12 feet on average. From the drop ceiling to the concrete of the floor above was another 3 feet. Allow 6 to 12 inches for the concrete and that will give you about 16 feet per floor. I think in mewer buildings it would be closer to 16 feet and probably 12 feet for older buildings.
Then you always have the odd floor, usually the first, that has the high atrium. that will throw you off.

When people say "x is y stories high" they usually mean approximately y times 10 feet (US) or y times 3 meters (metric). Even though, as RJK says, that's actually a little scant for a story in a real building.