To understand an airing cupboard, you must know that English houses do not have basements like American houses do. (That's why, where the steps go up to the bedrooms, there is a "cupboard under the stairs.") So - with no basement, - where do you put the furnace and the hot water heater?You don't *have* an American-style furnace - you have just a hot-water heater, which heats the water for the house, and also for the hot water radiators. (This is all assuming you've modernized and put in "central heating;" in olden days, the airing cupboard was empty except for the drying rack.)
The airing cupboard is upstairs, and is what we would call a closet; the one in my son's house is about 6x6 feet. It contains the hot water heater, which meams it is the warmest spot in the house, - thus, it is an "Airing Cupboard" - for the clothes which have not dried on the clothesline because it started to rain. The room is small, with just enough room for the water heater and a drying rack, (or a bit of canoodling by a pair of amorous young lovers!)
......courtesy of Meggie R. (who also adds these notes on the layout of the house):
The "cupboard under the stairs" is on the ground floor, in the front hallway. (We would call this the "first floor, but to the Brits it is the ground floor.) [This is where Jean and Lionel hide in a later episode.]The "airing cupboard" is on the first floor - what we would call the "second floor." We haven't seen one of these yet, it was just referred to [as a place where something of an intimate nature might have happened] "38 years ago."
The floor above that they might call "second," but usually it's referred to as the "attic," especially if it is the top floor. We would say "third." [Sandy's bedroom is in the attic.]
As for the place in the bedrooms where they keep clothing, etc., these are called cupboards as well -- not closets. They are normally free-standing pieces of furniture -- what we might call a "wardrobe." In newer homes they are sometimes built-in like an American closet, (but often still jut out into the room. Still they are referred to as "cupboards." [Lionel found a penny in a later episode in the cupboard in his bedroom.]