Java compliance refers to how well a Java program conforms to the Java standards set forth by Sun (now Oracle). Since the JDK^* is the standard Java development toolkit, programs developed using the JDK are guaranteed to be Java compliant.
If you should decide to use a third-party Java development tool, make sure that it is certified as being Java compliant. This is typically displayed prominently on the packaging. Most third-party tools have undergone stringent compliance tests and are safe to use.
One of the reasons compliance is such a big issue is because Java is constantly evolving, which requires development tools to also evolve and support Java's latest features and enhancements.
Another important compliance issue relates to the computing platform you are using; the JDK is currently only available for Windows and UNIX. However, third-party Java development tools are available for other platforms such as Apple Macintosh.
^* - Editor's note: JDK is the acronym for the Java Development Kit. Prior to Java 2, the Java SDK was called the JDK.