If you aren't familiar with the ability and trait system, here's the lowdown on how it works.
An ability is a follower bonus that specifically counters an enemy threat. Each follower you obtain falls under a particular class, and each class has a variety of various abilities that can be randomly assigned. When you choose a mission, you'll notice that most enemies have a threat that needs to be countered -- and while your followers can succeed without countering the threat, it's far more difficult to do so. To increase your follower's chances, you want to choose followers with the right ability for the mission at hand.
Traits, on the other hand, are special perks, buffs, or bonuses that your follower has. These perks vary in nature -- sometimes they'll increase success chance if that follower is paired with a follower of another type, sometimes they will grant that follower a bonus chance of success if they are completing a mission in a specific type of area or against a certain type of enemy. And sometimes, the traits are flat bonuses or buffs to your party -- reducing mission time, increasing experience gained, or even increasing garrison resources earned.
A follower can also have a Profession trait, which allows them to be assigned to a specific profession building. Assigning a follower to a Profession building is treated the same way as sending a follower on a mission -- while they are working at the building, you cannot send them on a mission. You can, however, have them stop working at the building at any time with no penalty. This is done via the Architect's Table in your garrison.
If you have a level 2 Inn or Tavern in your Garrison, it'll unlock the ability to recruit additional followers for your garrison at a rate of one per week. You can choose a specific ability or trait to look for, and the Headhunter will find three prospects for you to choose from. All of these prospects will include the ability or trait you requested, as well as a randomly assigned trait or ability to go with it -- and you can pick which one you like best. The only exception to this are followers with the Bodyguard trait. These followers are a very short list, and can only be found through quests or while traveling out in Draenor.
If you do happen upon one of the items mentioned in Crithto's post, be careful who you assign it to, because you'll lose a random trait in the process. While this doesn't matter so much with minor traits that affect things like mission location, it could very well mean you lose a follower that can be assigned to a particular building. If you're using these items, you'd be best advised to use them on followers that don't have any particularly appealing traits.