Here's an important definition, straight from the horse's mouth (FCC) - minus some editing to keep it simple: http://www.fcc.gov/mb/audio/bickel/haat_calculator.html
You can play with the calculator. It's fun, but watching TV is more interesting.
Antenna Height Above Average Terrain
is commonly used in the prediction of coverage by television stations. FM and TV coverage may be extended or shortened in a given direction depending on the terrain in that direction. For example, a mountain may reduce service (as compared to flat terrain), while a valley may allow expanded coverage. The HAAT value represents an average of the terrain elevations within 16 km (10 miles) of the transmitter site, and so provides a single value on which general coverage calculations and regulatory requirements (such as station classes) may be based.
This is what they base those service contours on. In other words, that mountain in the way may not affect the calculation, since it's "on average" not much of an impact. However, you may be the only one with the problem.
Height Above Mean Sea Level (MSL): That's how high the antenna is relative to the ocean (sea level). Pilots use MSL as a common reference so they know exactly where the hills and mountains are.
Height Above Ground Level (AGL): The height above ground level is how high off the ground the antenna is.
Antenna Height Above Average Terrain: 500. meters HAAT
Antenna Height Above Mean Sea Level: 510. meters AMSL
Antenna Height Above Ground Level: 0. meters AGL
From the above info, this antenna is sitting on a hill that is 510 meters above sea level. The antenna is 0 meters above that, so it's right at the top of the hill. Since the HAAT is at 500 meters, on average, the antenna can see 10 m over the top of the surrounding terrain.
WNET-DT's digital station, channel 61, is listed as a "construction permit" at 219 kW ERP (Effective Radiated Power) with an omni antenna. No clue why it's in the Canadian Border Zone (height can reach Canada?).
However, there are 2 listings for an STA (Station Temporary Authorization) at 2.66 kW. Check the service contours for these puppies. It's not a circle and covers NYC. I can't tell you which applications are active, i.e. which license applies?
(update from team_venture's info) This jives with team_venture's statements about the WTC / Empire State Building. The antenna is 0 m above the hill-top. In this case, the roof of a building.