You can get Lootbox's by Voting on the weekend's, Randomly while mining, Donating, and Inviting. You can use them by doing . There are 6 different types. Each give different items and cost a certain amount of keys which are all league based which you can learn more about in #discraft-info on the Official Discraft Server.
Type of Lootbox
Normal Lootbox 
Uncommon Lootbox 
Rare Lootbox 
Legendary Lootbox 
Ultimate Lootbox 
Mythic Lootbox 