Just to get this off the unanswered list...
A Hidden Ability is a rare Ability that Pokémon normally do not have access to, introduced in Generation V. Most Pokémon encountered in the games will not have a Hidden Ability; but usually, there are special encounter methods where Pokémon can have a Hidden Ability. Certain event Pokémon and special in-game Pokémon may also have their Hidden Ability.
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Essentially, it's a special ability that Pokemon normally found in the wild can't have, and are only obtainable through certain methods, listed here. Most Pokemon's hidden abilities are relatively uninteresting, but some are game-changing, such as Zen Mode on Darmanitan, (which allows it to change form) and Protean/Libero on Greninja/Cinderace.
Hope this helps!