Here’s the quick answer (Source: fedora project wiki) :
What is the Fedora Project?
The Fedora Project is a partnership of free software community members from around the globe. The Fedora Project builds open source software communities and produces a Linux distribution called “Fedora.”
The Fedora Project’s mission is to lead the advancement of free and open source software and content as a collaborative community.
Elements of Fedora’s Mission
The three elements of this mission are clear:
- The Fedora Project always strives to lead, not follow.
- The Fedora Project consistently seeks to create, improve, and spread free/libre code and content.
- The Fedora Project succeeds through shared action on the part of many people throughout our community.
Our Core Values
We strongly believe in the bedrock principles that created all the components of our operating system, and because of this we guarantee that Fedora will always be free for anybody, anywhere, to use, modify and distribute.