A static private method provides a way to hide static code from outside the class. This can be useful if several different methods (static or not) need to use it, i.e. code-reuse.
Static methods and static variables, sometimes called class methods and class variables, are a way of putting code and data into a kind of namespace. You could also think of class variables as variables attached to the class itself, of which there is (by definition) exactly one, instead of to instances of that class, of which there may be zero, one or many. Class methods and class variables can be useful in working with attributes that not just remain same in all instances, but actually be the same.
An example of a class variable is a database handler in an ORM entity object. All instances are their own object, but they all need access to the same database handler for loading and saving themselves.
Private versus public is a completely separate quality, which is I suspect what you’re stumbling over. A private method cannot be called and private variables cannot be accessed from code outside the class. Private methods are usually used to implement “internal” logic on the object that must not be accessible from outside the object. This restriction can be needed by instance methods as well as class methods.
An example of a private class method could be in a factory method. There might be three factory calls for creating an object which might differ in parameters being supplied. Yet the bulk of the operation is the same. So it goes into a private static method that the non-private factory methods call.