What are enums and why are they useful?

Question

Today I was browsing through some questions on this site and I found a mention of an enum being used in singleton pattern about purported thread safety benefits

Answer 1

Now why and what for should I used enum in day to day programming?

You can use an Enum to represent a smallish fixed set of constants or an internal class mode while increasing readability. Also, Enums can enforce a certain rigidity when used in method parameters. They offer the interesting possibility of passing information to a constructor like in the Planets example on Oracle's site and, as you've discovered, also allow a simple way to create a singleton pattern.

ex: Locale.setDefault(Locale.US) reads better than Locale.setDefault(1) and enforces the use of the fixed set of values shown in an IDE when you add the . separator instead of all integers.