Trait Essence allows you to apply rarer traits to your character. They're one of the main ways to add special traits, but they're only really good if you want to add one or two traits of a certain rarity. If you want to make something with a lot of rare traits, consider using a MYO Ticket.
Some items in this category can apply traits that are exclusive to that specific item, with no other way to get them, even from a MYO slot.