IPB is forum software that used to be freeware. You used to be able to get version 1 and the 2 betas for free but recently, it was taken down and switched over to pay-only. Boo! But those of us who already have it installed are still using it and we still have the installers
If someone wants it that doesn't have the installers and can't find it, you can ask me and I will upload them somewhere.
The forum uses PHP and mySQL server side to generate what we see and store what we put in. This is one of the more robust, feature-rich forums out there. If you'd like something else, I suggest phpBB. It isn't as stable but it does have a large amount of features and is open source so its always getting new stuff.