Why is alcohol useful?

It's a very useful antibacterial and is often used in hand gel etc as a disinfectant.

Alcohols (note the 'drinkable' alcohol is ethanol, which is one of many alcohols) also tend to burn cleanly, notably methanol and ethanol.

The most common use outside of being drunk and used as a disinfectant is probably either in perfumes (and colognes/eau de toilette) or to dissolve substances such as vanilla extract.