bbPress is a WordPress plugin that adds forum functionality to WordPress. Essentially, it lets you create a full-featured forum as: Your entire WordPress site. A small part of your existing WordPress site.
You can quickly set it up for a place for asyncronous discussion, subscriptions, and more.
bbPress takes advantage of the WordPress user management system.
bbPress started because miniBB was too bloated for the WordPress support forums. In 2004 the WordPress team decided to code a completely new forum system from the ground up. It was first published on WordPress.org and since then it has been turned into a plugin. Most basically it is used as forums, light weight and can easily blend into a WordPress theme. It was created by the same people who created WordPress so it follows the same principle of keeping things small and lightweight.
bbPress is intentionally simple yet infinitely powerful forum software, built by contributors to WordPress.