A Hidden Ability is a special ability of a Pokémon that cannot normally obtain in the wild. Every Pokémon has one. They were introduced in Generation 5. Hidden Ability's usually make the Pokémon stronger.
How to obtain
In Generation 5, the Hidden Abilities were only obtained from Pokémon obtained via Dream World. Participating in these web based games could earn the player special Pokémon that they could bring over to their games. Some Pokémon never were released in this format although they were shown to have Hidden Abilities via hacking. In addition, due to the Nintendo shutting down Wi-Fi functionality, the Dream World service was shut down so, Pokémon cannot be obtained this way.
In Generation 6, there are two methods for finding them. The first, is randomly during Horde Encounters. Randomly, there may be one or more with a hidden ability. However, this is limited to only Pokémon found in hordes. Any other Pokémon relies on a different method. This method is using the Friend Safari. The Friend Safaris contain up to 3 random Pokémon of a certain type. Pokémon occasionally will have this hidden ability but this is still rare.
In addition to these ways, Pokémon can breed down the ability.