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

So far, I have never needed to use enums. I have been reading about them since they were introduced in 1.5 or version tiger as it was called back in the day. They never really solved a 'problem' for me. For those who use it (and I see a lot of them do), am sure it definitely serves some purpose. Just my 2 quid.