Polymorphism is a feature that allows a given statement to do different things. In COBOL, the ability for a data item to contain various objects of different classes means that a method invocation on that data item can be bound to one of many possible methods. Sometimes the method can be identified before execution, but in general, the method cannot be identified until run time.
A data item can be declared to contain objects of a given class or any sub-class of that class; it can also be declared to contain objects that conform to a given interface. When a given interface is used, the classes of the objects may be completely unrelated.