bbPress is free, open-source forum software designed to work seamlessly with WordPress. It can be installed as a plugin and provides an easy way to add a discussion board to your site while still maintaining the simplicity and flexibility of WordPress.

From https://bbpress.org/about/

AboutThe SkinnybbPress is forum software, made by the WordPress community.Have you ever been frustrated with forum or bulletin board software that was slow, or full of features you don’t need? bbPress is focused on simplicity, flexibility, a deep integration with WordPress, web standards, and speed.We’re keeping things as small and light as possible while still allowing for great add-on features through WordPress’s extensive plugin system. What does all that mean? bbPress is lean, mean, and ready to take on any job you throw at it.
 Philosophy
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Every line of code is written with these principles in mind, and if that sounds good to you get involved!The TeambbPress is a GPL licensed open-source project made possible by thousands of contributors and believers around the world. Patches and RFC’s are helpful and encouraged, and props are given and gathered for each contribution.

From https://bbpress.org/about/features/

Features
We can’t list everything bbPress can do, but here’s a few of our our favorite features.

Simple Setup
Easy to setup. Easy to moderate. Fast, and clean.

Fully Integrated
One central account. One unified admin area. One click install.

Single Installation
Simple step-by-step installation walks you through your options.

Multisite Forums
Divide your site into sections. Allow your users to create content.

Fast and Light
We keep our code lean so that you get the best experience possible.

Familiar Interface
One of our biggest goals is to keep things simple and make things intuitive. Our dream is that you forget you’re even using the software.

Customizable Templates
Not everybody likes the same pair of pants, so we allow you to dress up your forums however you like.

Highly extensible
bbPress can’t toast your bagels, but a plugin for it sure could!

Spam protection
Full Akismet support built in offering you an amazing weapon against spam.

RSS Feeds
You want feeds? We got ‘em! They’re everywhere!