Hmm.... well, just in case it's not clear enough.... and because I'm bored atm...
The Dream Chests are unique in that there is a limited number of specific cards you can draw from it, unlike the standard packs which the choices are unlimited. The more unwanted cards you draw from it, the more likely you'll get to obtain your favourite card from it (mostly, it'd be the 7*).
When you spend on a Dream Chest pack, the cards you receive from them will deduct from your 'track record' or your list of available cards you can get from the Chest.
For example, one of the packs you buy gives you 8 4*s & 2 5*. The 6 4* cards you got will be subtracted from your record of 1230 to 1222. The same goes for your 1 5*, from 100 to 98. Since they haven't displayed what specific cards you'll only get from 5* selection, it means you can draw that same card again, when you buy another pack. Once the 4* record drops to 0, you will not be able to draw anymore 4*s from the Chest.
If you draw one of the 6*s they are available for that Dream Chest, that card will not show up again, giving you the chance to get one of the other 6*s available instead.
That's where the 'Reset Chest' function comes in. If you got the 7* card but want to get another one, hitting that button will restock the Dream Chest to full once again. Of course, that means you'll have to go through the 4*s & 5*s again.
Also, you can only get 3* cards if you use the Dream Tickets on the Dream Chest packs. Those who pay for the packs with Coins/Points don't have to see their chances wasted on 3*s.