What is a runway?
A runway is a defined area used for aircraft take-off and landing. It can be paved or unpaved. On numbered runways, the number indicates a direction rather than a name.
Runways need not be paved. The CAA's take-off guidance explicitly distinguishes grass surfaces from paved surfaces. A grass runway is still a runway; the surface and the direction marking are separate questions.
The rule is exact. The FAA's Aeronautical Information Manual states that the runway number is the whole number nearest one-tenth the magnetic azimuth of the centerline of the runway, measured clockwise from the magnetic north. Magnetic, note, not true. A strip pointing due east is Runway 09, and the same strip walked back the other way is Runway 27. Where there are parallels, an L, C or R is added.
Because it's magnetic, the number can change without the tarmac moving. Magnetic north drifts, and when it drifts far enough an airport has to repaint.
Why the runway in use keeps changing
The wind. Heathrow's own explanation of its operations says that for safety and performance reasons aircraft typically take off and land into the wind, and that the direction aircraft fly there depends on the wind direction, with air traffic control deciding. A headwind means lift builds sooner on the take-off roll and the landing roll is shorter.
For anyone standing at the fence this is the single most useful thing to know, because the runway in use decides whether you spend the afternoon photographing noses or tails. There's more of that in the plane spotting photography guide.
Every runway sits at an airport with a code, which is what an airport code is. An aerodrome reference code describes design categories instead of identifying the airport. The rest of the ground is covered on the sky.
