What exactly is a Class Factory?

Question

I see the word thrown around often, and I may have used it myself in code and libraries over time, but I never really got it. In most write-ups I came across, they just went

Answer 1

A class factory constructs instances of other classes. Typically, the classes they create share a common base class or interface, but derived classes are returned.

For example, you could have a class factory that took a database connection string and returned a class implementing IDbConnection such as SqlConnection (class and interface from .Net)