The feed dogs are the little toothy bars under the needle plate that pop up and pull the fabric away from you.
Free-motion is when you are guiding the fabric instead of letting the feed dogs guide it.
You can make straight or curvy lines in any direction you choose, creating designs of your own.
If you can drop or cover the feed dogs, there is one less thing to interfere with your movement of the quilt or embroidery under the needle.
The 301 is a much stronger machine than the Featherweight and it has a much bigger open area under the arm of the machine, allowing you to work in the middle of even very large quilts. The vertical bobbin arrangement is optimal for free-motion quilting - it is very forgiving of the sudden and frequent changes in directions that you might make in free-motion quilting. It's not as cute, but it's much more versatile. :)