Big Kahuna Hosting is using Simple Machines for this forum.
Unlike many of the other Free To Use forum applications, Simple Machines actively supports and updates this application. It serves the needs of about 90% of the people wanting a easy to use/administrate forum. The other 10% needing more features should consider vbulletin. Simple machines will require on database and is most often installed in a directory called forum or forums.
If you're uncomfortable installing into you hosting account, the Big Kahuna can install and set to automatically upgrade as new releases come out.
http://www.bigkahunahosting.com/hosting-services/ (http://www.bigkahunahosting.com/hosting-services/)