Outfits and Headgear are cosmetic only items. You can select 1 out of 4 outfits at the character creation screen. You can obtain outfits by completing some Pursuits, some Missions or purchase them from the game store.
Outfits are the entire appearance from the neck down and Headgear is the head only.
Devil's Carnival Crate from the Bit Store
7th Legion Supply Crate from the 7th Legion Faction vendor at Overpass.
Abominable Warmaster Pack during Solstice Strike.
Abominable Warmaster Pack during Solstice Strike
Chance from Corporate Espionage Lockbox
Rewarded from pre-ordering the Digital Deluxe Edition
Digital Deluxe Edition (Pre-order)
Outlaw Supply Crate from the Defiance Store