JRE is the Java Runtime Environment.
You need that application to run Java programs and applets.
You can download it here if you don't already have it:
http://java.sun.com/
To see if you have it installed, go to the controlpanel and
look for a Java Plugin. If there isn't that icon displayed, you probably need to download the JRE.

If you already have the JRE, check if it is the newest version.
(1.4 I think)