Method overloading and method overriding are core concepts in Java's object-oriented programming. Method overloading occurs within the same class when two or more methods have the same name but differ in parameters (type, number, or both). It enhances code readability and flexibility. Method overriding, on the other hand, happens in a subclass where a method from the parent class is redefined with the same signature to provide specific behavior. Overriding supports runtime polymorphism, enabling dynamic method resolution. Overloading is used for code variation, while overriding ensures behavior customization in inheritance. These concepts are essential topics in any Java certification course.