Holy Keyblade! how did you get so many? or did you just not use them until now?
of course they're good for something xD 1 of those = 1 card. The first (golden) ones give you SR+ cards, the other ones give you SR cards. You choose between Attack cards or Assist cards, and then you'll get 1 random card from the lists of available cards (the little blue buttons show you which cards are available).
You see there are 2 sections in the Mog Medal Shop screen, one for the SR+ medals (at the top) and one for the SR medals (bottom). To use a Mog Medal you click the red button in the section you want. The red buttons under the golden text (left) give you Attack cards, while the red buttons under the white text (right) give you Assist cards.
but I assume you already knew this, so, now for something different..
Beginning with the SR medals. Use them up and you'll eventually get all the cards from the SR section, both Attack and Assist. Continue using the SR medals up and you'll get the same cards, so you can Limit Cut the first ones. Once you get those SR cards to High Purity, you sell them and you'll get SR+ medals.
Now, with the SR+ medals it's basically the same thing, use them up and you'll get all the cards. The cards you get will repeat and you will be able to Limit Cut them till they reach High Purity. But here's the nice part: SR+ cards can be transformed into Ultimate cards, and then you can continue strengthening them to crazy stats.
Here's KHI's guide for Ultimate cards:
http://forums.khinsider.com/kingdom-hearts-chi/200731-ultimate-card-system.html
Ultimate cards = strong cards = stronger you = totally trashing LV666 Event Heartless = more rewards = even stronger cards = more LUX = higher rank = even more power = even more rewards etc.