What Is A Class With A Private Constructor Called In Java?

Constructors by default are public..
They can be declared as private in case of the singleton classes and   also if the class contain all the constants.singleton classes are those for whom only one object could be made.
In this case when you try making the second object it displays an error..

A singleton, a utility class such as a Factory

We cannot instantiate the class by another class. It's the main use

Generally by making a constructor as private one can't instantiate the class by creating objects.The following classes generally will have private constructors they are abstract classes and singleton classes.

Private constructors can be used in two ways, private constructor can be called by other constructors.
or private constructors can also be called from static methods.

To call a static method on a class you don't need an instance.
So a static method inside the class can create an instance of the class(Static method is inside the class so it will have access to private constructor also).