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.
i have already my deck of SR+ (i'm ultimizing it, with 2 60k/60k and a third coming in few minutes). and i know about the medals XD
i just wasn't using them cause i had 340/350 card in my collection, so no room for other card (i left some space for the materials).
and i'm also "collecting" raise ticket (more than 40 at the moment) in hope of getting one (or more) POWER sr+ card with COMBO ex, when they give it again...
I've pretty much been ignoring the things for the past few months. It's too tedious to cash over a hundred card medals in a row, then HP them, then recycle the SRs, then cash another hundred card medals, all while dancing around the fact that I only have about 50 slots open in my deck, then wish I was playing a game with a better GUI, then realize I'm out of Ultimate cards that need junk cards (I really just need Moogles), and then realize I just wasted my time.
Of course, I've been falling further and further behind in this game since the Ultimates were introduced, so I'm probably not a good model to emulate.