This is what I came here to learn. I assume you end up getting a few extra things out of a merged set than you would if you just used them each individually. For example 1 would maybe give you 10 items but a merged would possibly give you 23. Not sure if it gives you different or better items though.

I used mine to buy extra inventory spaces. Also when you select charging items on the board, the info bar tells you want you can do with the gems. You can use them to skip a charge time