There are three options:
Once you register a security key, the login prompt may still say it's optional, but no longer is at that point. Once a security key is registered, it must be used for all future logins.
Both types of keys display a 8 digit number that you type in yourself into the appropriate field in launcher login. It does not require any kind of USB connection or anything.
It is either a physical device (fits on a keychain, etc.) or an app on your mobile device. So it isn't really "moved between" computers; just carried by you. Depending how heavy your mobile device is, and how weak your biceps are, it still shouldn't be much of a problem. :)
Once you login with a registered security key, you will then get access to the in-game security key vendor. Mostly it offers the ability to purchase with in-game credits some, but not all, of the items that come with Collector's or Digital Deluxe editions. See the short list here. "Some examples of the items are the (popular so far) fleet pass which allows you to return to the fleet, a mouse droid (different skin from the Collector’s Edition item), Exchange Bandit (Increase movement speed by 110% Requires: Speeder Piloting Rank 3) and more."
Also see the official site page describing the security keys.