Java classes and objects are fundamental concepts in object-oriented programming. A class defines the attributes and behaviors of a type of object, acting as a blueprint. An object is an instance of a class, having state stored in fields and behavior through methods. The document provides examples of defining a Dog class with name, breed and color attributes, along with behaviors like barking. It also demonstrates creating Puppy objects, setting fields, and calling methods. Constructors initialize new objects, and classes can contain variables, methods and constructors.