Mystery Boxes are containers of (nearly) unlimited prize possibilities. You can either purchase your own Mystery Boxes through the Dungeon Shop, spend your Dungeon Points (see Maps and Dungeons for more information), or you can get lucky and win one through the Daily Midnight Lottery (minimum level of 100 is necessary to be eligible to win). Nothing is required to enter, just be logged into the game within the last 24 hours prior to the drawing at Midnight server time, and you have a chance to win. :) You can also get one rarely from your Daily Reward.
Once you purchase or win a Mystery Box, it will be available to be opened in your Inventory. Opening it will give you a random prize, ranging anywhere from 1 copper to an Exquisite orb. Out of the types of prizes you can win, there are ranges that qualify either as a Booby Prize (basically a dud, that has its own Ranking), a Global, or in between. Below are each type of prize available, and their ranges:
Mystery Chests can be gained either from opening Pandora's scratch cards, converting mystery boxes into chests at a rate of 12 boxes to 1 chest or by random luck at the daily reset. Mystery Chests function much the same way as Mystery Boxes, with a few notable differences. These are:
cost 10,000 Dungeon Points each.10 random rewards from the mystery box pool, you could receive 10 of the same exact prize, or 10 completely different ones.