It is a ability of a pokemon that can only be obtained, in X/Y through horde battles or the Friend Safari (You must be online at the same time as the Friend Safari you are exploring is online for Hidden Ability Pokemon to appear).
Some pokemon do not have hidden abilities, most do.
Previously the only way to obtain hidden ability pokemon is to play the Dream World but that had been closed due to arceus dying, and the death of a god ravaged the pokemon world and the real world.
You can not use Ability Capsule to change to Hidden Abilities it is only used to switch between your primary and secondary abilities.
You can breed your pokemon for hidden abilities.
Female Pokemon with Hidden Ability must not be bred with Ditto or else they can not pass down their hidden ability. They must breed with a non ditto to have a 80% chance of inheriting their Hidden Ability.
Male Pokemon with Hidden Ability must be bred with Ditto to have a chance to breed a pokemon with the hidden ability such as Torchic.
You can not breed a pokemon to have a hidden ability if you do not have at least one parent that has the hidden ability.
When a pokemon with their hidden ability evolves, then the evolved pokemon will get their hidden ability. (Ex: Dratini (Marvel Scale) -> Dragonair (Marvel Scale) -> Dragonite (Multiscale))
With courage comes glory. With glory comes immortality.
Hidden power is a 60 base power TM move that most pokemon can learn. Depending on the pokemon's IVs (internal stats that are hard-set and unique for each individual pokemon), they will have a different type hidden power. So a pokemon who normally uses water attacks could have a fire hidden power, but breeding another pokemon of the same species may result in a monster with flying hidden power.