Emerald

"Ah, to be minted with the green stuff. To swan about the villages of the Overworld with pockets bursting with emeralds. “Ho there, villager!” you would bellow, tossing a few emeralds for a handful of carrots. You’d never need farm again!"

- Alex Wiltshire

Emeralds are an uncommon material, and are the currency used in villager trading.

Mining
Emerald ore is mined using an iron or diamond pickaxe and will drop one emerald. If the pickaxe is enchanted with fortune, it may drop an extra emerald per level of Fortune, up to a maximum of 4 with Fortune III. If the ore is mined using a pickaxe enchanted with Silk Touch, it will drop itself instead of emeralds.

Natural generation
In Pocket Edition they can also be found in village blacksmith chests.

Drops
Vindicators and Evokers will drop 0-1 emeralds upon death.

Trading
Emeralds are primarily used as currency for trading with villagers. Trading is a much easier and less time consuming way to obtain emeralds than mining is.