bzip2 is a compression program.
The bzip2 KIO worker is not directly usable, and is intended for use
as a filter. For example, the tar KIO worker can filter a file through
the bzip2 KIO worker, in order to display the contents of a
tar.bz2 file directly in a Konqueror
If you click on a file compressed with a
.bz2 in Konqueror, this KIO worker is used to
uncompress it and display it as a normal (uncompressed) file.
If you are a developer, and would like to use the bzip2 filter, you can find documentation on using KIO workers at http://techbase.kde.org
See the manual: bzip2.
bzip is the ancestor of bzip2. It is rarely used today, having been replaced with bzip2, which offers much better compression.