What does this mean? Is it to download Blender Files from the course? For example....if it is discussing Rigging....would it be to download an armature from which i can use to practice rigging?
Short answer is yes. Not all courses have downloadable files, but most of them. It's to provide you with different assets if you want to follow along with a course. There's also a download section here with other extra stuffs apart from course files:
https://cgcookie.com/downloads
Typically courses will have their course files where it says course files:
This course only has that course file in it:
Other courses will have other course files.
Exercises have a dedicated lesson which will guide you through on what to submit and how to submit. When you reach that point you'll come across one and have some fun with it.