Download the latest SDK or JRE from http://java.sun.com/j2se/downloads.html. If you plan to do java development or to build jEdit from source, get the SDK, otherwise get the JRE. There is no reason to get both because the SDK contains the entire JRE. The SDK is also commonly called the JDK.
Mac OS X users may want to get 1.3.x instead as 1.4 is still buggy