Singleton: How should it be used

Question

Edit: From another question I provided an answer that has links to a lot of questions/answers about singletons: More info about singletons here:

So I have read th

Answer 1

I still don't get why a singleton has to be global.

I was going to produce a singleton where I hid a database inside the class as a private constant static variable and make class functions that utilize the database without ever exposing the database to the user.

I don't see why this functionality would be bad.