JVM means Java Virtual Machine. This is the program which interprets and compiles the Java byte code of an Java application into native code.
It's basically the same in the two downloadable Javas: JRE and JDK.
- JRE is the "Java Runtime Environment". It just contains the mentioned JVM (basically). A user who wants to run your Java application needs the JRE. It's about 12-14 MB in size to download. You could also bundle the JRE with your application, though.
- JDK is the "Java Developer Kit" which is just needed by developers. It contains the JRE plus compiler, debugger, and more tools for developers. A user normally doesn't need it.
Don't miss the Java Tutorial. Together with other interesting books about the JVM and so on they're available here:http://java.sun.com/docs/books/
(Those books with a monitor icon can be read online.)