Simple Machine Forums (SMF) is a PHP scripts that will enable a forum on your website. It is very easy to install and offers a variety of administration options, although aren't very well organized.
SMF is a very popular free solution that offers the essential administration tools, but the menu is not very intuitive and often confusing.
This CMS has a large success and is used by thousands of forums. It is free and has a large community, but we have found that the admin panel is not very intuitive from the first use so you may need some time to get used with it.