What are Runway Declared Distances?
From the AIM, 4-3-6 (c)(2):

All 14 CFR Part 139 airports report declared distances for each runway. Other airports may also report declared distances for a runway if necessary to meet runway design standards or to indicate the presence of a clearway or stopway. Where reported, declared distances for each runway end are published in the Airport/Facility Directory (A/FD). For runways without published declared distances, the declared distances may be assumed to be equal to the physical length of the runway unless there is a displaced landing threshold, in which case the Landing Distance Available (LDA) is shortened by the amount of the threshold displacement.

Now for definitions. These terms are defined by the FAA/ICAO in the PCG.
TODA - Takeoff Distance Available. The takeoff run available plus the length of any remaining runway or clearway beyond the far end of the takeoff run available.
TORA - Takeoff run available. The runway length declared available and suitable for the ground run of an airplane taking off.
ASDA - Accelerate-Stop Distance Available. The runway plus stopway length declared available and suitable for the acceleration and deceleration of an airplane aborting a takeoff.
LDA - Landing Distance Available. The runway length declared available and suitable for a landing airplane.
(also Declared Distances from wikipedia)
which lead to other definitions...
Stopway - An area beyond the takeoff runway no
less wide than the runway and centered upon the
extended
centerline of the runway, able to support the
airplane during an aborted takeoff, without causing
structural damage to the airplane, and designated by
the airport authorities for use in decelerating the
airplane during an aborted takeoff.
Clearway - An area beyond the takeoff runway
under the control of airport authorities within which
terrain or fixed obstacles may not extend above
specified limits. These areas may be required for
certain turbine-powered operations and the size and
upward
slope of the clearway will
differ depending on
when the aircraft was certificated.
then for those specified limits of the clearway, in 14 CFR Part 1 we find

Clearway means:
(1) For turbine engine powered airplanes certificated after August 29, 1959, an area beyond the runway, not less than 500 feet wide, centrally located about the extended centerline of the runway, and under the control of the airport authorities. The clearway is expressed in terms of a clearway plane, extending from the end of the runway with an upward slope not exceeding 1.25 percent, above which no object nor any terrain protrudes. However, threshold lights may protrude above the plane if their height above the end of the runway is 26 inches or less and if they are located to each side of the runway.
(2) For turbine engine powered airplanes certificated after September 30, 1958, but before August 30, 1959, an area beyond the takeoff runway extending no less than 300 feet on either side of the extended centerline of the runway, at an elevation no higher than the elevation of the end of the runway, clear of all fixed obstacles, and under the control of the airport authorities.