What kind of items are you supposed to put in there?

Any and all items can get in there, providing they're between rarity 1 and 99. Just know that you're only guaranteed getting a crystal in return when the rarity is at least "rare". If lower, you have a bigger chance of not getting a crystal than actually getting one.

As Efinesse has said, all restockable items can be put into the fragmentizer. It's tougher to get a crystal from mundane, really common, common, and normal items, but not impossible. Rare items are guaranteed one crystal. Super rare items are guaranteed one, and have a chance of giving you an extra crystal for a total of two from one super rare item.

Okay thanks to both of you for the help!