Each species has three ability slots. Two of these are reserved for abilities that the species could have when you encounter it under normal circumstances. The third is the hidden ability (HA).
For example, Nidoking has the following slots:
- Slot #1: Poison Point
- Slot #2: Rivalry
- Hidden Ability: Sheer Force
Sheer Force is "hidden" in the sense that Nidoking will never be spawned with Sheer Force under normal circumstances. Once you do get a Nidoking with Sheer Force (which would require some special technique or encounter method), there is nothing hidden about it. The game will show it in menus like any other ability.
In case it isn't clear, a Pokemon can only have one of its species possible abilities at once. HAs are not additional abilities.