Polymorphism in Java allows an object to take on multiple forms. There are two types of polymorphism: compile-time polymorphism (method overloading) and runtime polymorphism (method overriding). Method overloading involves methods with the same name but different parameters, while method overriding involves subclasses providing their own implementation of a superclass method. Abstract classes allow defining methods without implementation, requiring subclasses to implement them, while interfaces only define method signatures that implementing classes must then define.