If you’re hot off of playing recent entries in the Fire Emblem series such as Awakening or Fates, your brain is most likely completely calibrated to think about (and probably obsess over) Skills. Skills are great, and are retained in a passive form in Shadows of Valentia. Still, there’s a separate system you’ll need to focus on, as Skills depend on weapons and items to function.
The unique thing about Passive Skills is that they’re derived from weapons and held items. Unlike Combat Arts, which require continued use of particular weapons to "unlock," Passive Skills are immediately available upon wielding the weapon they're associated with. For example, if Celica wields a Blessed Sword, she'll have instant access to Recovery, restoring 5 HP at the start of each turn. If she unequips the item, the Passive Skill goes away.
The good thing about Passive Skills is that unlike Combat Arts, they're instantly accessible via items and thus can be passed between similar units easily. The downside, though, is that the held item in question needs to be held for their continued use.
Passive Skills are activated automatically and continuously when a corresponding item is held, hence their name.
For a full list of all Passive Skills, click here.