Even if a Pokémon has the Ability you desire, it will almost never have all traits that you want, such as the correct nature and IVs. To get all of these traits on one Pokémon requires breeding. So even if you have a Pokémon with its Hidden Ability, chances are it doesn't have the right nature or IVs, unless you got it from a trade and it has been bred by someone else. If you want a Pokémon that does have the right nature and perfect IVs, with the Hidden Ability, you need to breed, and pass down the HA to get better Pokémon.
Basically, the offspring won't be the same as the mother, people who breed are competitive battlers, which means they will be breeding for the right natures and perfect IVs too, until they get a "perfect" Pokémon.
For example, let's say I caught a Weavile with its Hidden Ability, Pickpocket. It has a Modest nature, and no perfect IVs. I want an Jolly nature for this Weavile, and have 31(max) IVs in every stat except Special Attack, and I also want the Hidden Ability.
To get all of these things on one Pokémon, I will have to breed. Let's say I happen to have anither Weavile with a Jolly nature with 3IVs, but no Hidden Ability. This Pokémon has a Jolly nature, which can be passed down to the offspring if it holds an Everstone. Now that the nature's sorted, we'll turn to IVs next. By giving the original Weavile(the one with the HA) a Destiny Knot, it will pass down 5 random IVs from either parent. This means that the more perfect IVs the parents have, the higher the chance of the offspring getting perfect IVs. After this, I just keep breeding and hatching eggs, switching any offspring that have superior IVs than the parents for them. It may take a while, as breeding usually does, but eventually I will get a Pokémon with all the right traits I want, Ability, nature, IVs. If everything goes well, I will have a Jolly Sneasel with 5IVs and its Hidden Ability. Another thing people might breed for is egg moves, but I won't go in to that.
To read more on breeding, look here.