What is Free and Open Source Software?

At its core, Free and Open Source is centered around four linked freedoms (text mostly from the Free Software Foundations' Free Software Definition):

The freedom to run the program, for any purpose.
The freedom to study how the program works, and adapt it to your needs.
The freedom to redistribute copies so you can help your neighbor.
The freedom to improve the program, and release your improvements to the public, so that the whole community benefits.

“Copyleft” (e.g., the GNU GPL) can be used to protect these freedoms from enclosure.