Limewire is written in Java. Java sits on top of the OS of the host machine (Windows, Mac OS, Linux etc) and the software (such as Limewire) works in Java.
Its main advantage is that it is multi-platform - software written in Java will work on any computer with a compatible version of Java installed.
Its main disadvantage is that Java software is slower than native programs.
More information and downloads:
http://java.sun.com/