I know that the empennage is the tail section of the aircraft and includes the horizontal and vertical stabilisers. But what is the empennage height? Is it the height of the horizontal stabiliser from the ground or is it the height of the vertical stabiliser?
Of the two possibilities you mentioned, the most likely is the height of the top of the vertical stabilizer from the ground with the plane parked normally. For conventionally-configured tricycle-gear airplanes, this point is the tallest on the aircraft, and therefore this height is useful in determining the required clearance for covered parking areas and hangar openings.
There are a few designs for which a different height measurement is needed. A tail-dragger's tallest point will usually be either the cockpit or a point in the prop's sweep (more likely the cockpit for civilian designs, more likely the prop for old warbirds). The Predator drone uses an inverted V-tail, and its tallest point is actually its communications antenna. The Beechcraft V35 Bonanza's tail tips are within a couple of inches of the top of the cabin. In all these cases a "parked height" figure is required which will be greater than that of the vertical stabilizer.
The empennage height is the distance from the ground to the top of the tailfin.
It determines the minimum clearance the aircraft needs to taxi under an obstruction.