A static member function in C++ is a function that is declared as static within a class. When a member function is declared as static, it becomes independent of any object of the class and can be called even if no objects of the class exist. Static member functions are accessed using only the class name and the scope resolution operator.

Some key features of static member functions include:

• They are independent of any object of the class.
• They can be called even if no objects of the class exist.
• They can be accessed using the class name and the scope resolution operator.
• They can access only static data members and other static member functions inside or outside of the class.
• They do not have access to the this pointer because they have class scope.

Static member functions are useful for maintaining a single copy of the class member function across different objects of the class. They are also useful for declaring global data which is shared across all objects of the class.