Classes in Java represent templates for objects that share common properties and behaviors. A class defines the blueprint for objects, but does not use memory itself. Objects are instances of classes that represent real-world entities. For example, Dog is a class while Tommy is an object of the Dog class. Classes contain variables that store object data and methods that define object behaviors. Objects are declared by specifying the class name and are initialized using the new operator, which allocates memory and invokes the class constructor.