The Java Virtual Machine (JVM) acts as a mediator between operating systems and the Java programming language. When Java code is compiled, it produces bytecode that can run on any system with a JVM. The JVM interprets and executes the bytecode, generating output for the underlying operating system. Classes in Java contain fields to store data and methods to operate on that data. Objects are instances of classes created using the new operator, and constructors initialize objects when they are created. Exception handling uses try/catch blocks, where exceptions thrown in the try block can be caught and handled in catch blocks.