Why does age improve alcohol?

Alcohol is a simple chemical compound and does not change with age. Sugars are also very stable and don't change with age.

Beers and wines age in the bottle because some of the compounds that contribute to their flavor undergo chemical reactions. Some wines improve with age -- strong reds in particular can become more mellow. A few very strong beers also benefit from some aging. However, all beers and wines will eventually degrade in the bottle and become undrinkable.

Distilled spirits do not age if kept from air and light. However, whiskies and some other spirits are aged in wooden barrels. The interaction of the liquor with the barrel causes changes in flavor and color, as compounds leach out of the wood. Some wines and beers are also aged in wood for a time.

There are only two types of alcoholic drink I know of associated with "ageing" - wine and (some) sprits, especially whiskey.

Most of a bottle of wine is not alcohol. In some cases less than 10% of the wine is alcohol. Once bottled, the various constituent parts of the wine - acids, tannins and sugars become smoother and blend togther in a way that, to most people, results in a subjectively "better" flavour. However, wine is not intended to be aged for long - the majority of commercially produced wines are intended to be drunk within a year of bottling and will deteriate after that. Old bottles of wine are valuable not because ageing has made them taste better but because they were valuable to begin with and have become rare - they are collected in the same way as a person might collect antiques. It is very unlikely that a really old wine would even be drinkable.

In the case of sprits, it is mainly whiskey and some brandy where aging is an issue. When first distilled, whiskey and brandy are clear (like vodka, which is not aged). The amber colour results from the spirit being stored in, for example, oak casks (the insides of which are sometimes charred). Being allowed to "rest" for some time does, to most people, improve the taste. The whiskey or brandy also takes on some of the character of the cask in which it was stored. Flavour is a very subjective thing but most people prefer the taste, look and aroma of a whiskey or brandy that has been stored in this way for some time. It is only good quality spirit which is stored in this way for any length of time. Obviously storage takes up space and costs money. Therefore, the older the spirit the more it costs and, generally, to most people, the better the taste.

It has nothing to do with any sugar contained in the drink or, as one person suggests, the fermenting process. Most people would not like the taste of whiskey or brandy straight from the still. Aging makes it smoother and better tasting, at least "better" in most people's opinion.

Cheeses too are aged and so are some cuts of meat.

It doesn't improve alcohol. Alcohol is alcohol. It improves SOME wines and makes SOME spirits more mellow and complex.

Most wines are intended to be drunk within one or two years.

It's basically just a marketing ploy, similar to primer in "paint and primer"

I'm not sure how to answer this. It must have to do with the fermenting process. I know that wine ages, but eventually turns to vinegar. Whiskey gets smoother when it ages. Ultimately it's about taste. And Pepsi doesn't age because it isn't fermented. I'm not sure why beer doesn't age now that I think about it.