Each player has four chest slots, so you can only have up to four chests waiting at a time. Alternatively, the wait can be skipped using Gems/Chest Key or hastened using boosters upon reaching a new Arena or League.
Unlocking a chest takes a certain amount of time.
Chests are won from battles and must be unlocked before you can receive their contents. You can earn Chests to obtain Gold, Gems, Cards, and Wild Cards.