I saw this beacon at an old airport; how and in what situations was it used?
It's the airfield identification beacon.
An aerodrome beacon or rotating beacon is a beacon installed at an airport or aerodrome to indicate its location to aircraft pilots at night.
An aerodrome beacon is mounted on top of a towering structure, often a control tower, above other buildings of the airport. It produces flashes not unlike that of a lighthouse.
Airport and heliport beacons are designed in such a way to make them most effective from one to ten degrees above the horizon; however, they can be seen well above and below this peak spread. The beacon may be an omnidirectional flashing xenon strobe, or it may be an aerobeacon rotating at a constant speed which produces the visual effect of flashes at regular intervals. Flashes may be of just a single color, or of two alternating colors.