Java is the language that a lot of applications are written in. Java script and applets are written in java. All computers run Java but the problems can arise through Java script which is like a subset of the Java language. Lots of popups and little applets are written in Java.
These little popups and java script is where some viruses can be spread from. If you disable applets and java script you may protect your machine more but you will not be able to see all those popups.
Personally I wouldn't visit the site until the problem has been absolutely fixed and don't click on the popups.
