Type is the term used to refer to how an attacker performs an attack in Super Smash Bros. Brawl, Super Smash Bros. for Nintendo 3DS, and Super Smash Bros. Ultimate. For example, using an arm to attack makes it an Arm attack.
In Super Smash Bros. Brawl, the concept is tied to how stickers are used in The Subspace Emissary to power up attacks of a certain type. In Super Smash Bros. for Nintendo 3DS, the concept is used by powers in Smash Run. In Super Smash Bros. Ultimate, Spirits can power up attacks of certain types, and some conditions in Spirit Battles boost the power of certain attack types. Types have no significance outside of these cases.
The origin of the term "type" is unclear. While Toomai coined the term upon discovering the coding of the feature, he does not recall why he chose it, given that "type" is used by other series (such as the Pokémon series) to refer to what is known in Smash Bros. as effects.
List of types
Evidence suggests that, while not all types have corresponding Smash Run powers, the underlying data structure remains the same as Brawl, and so all types in Brawl are also in SSB4. There is currently no evidence of new types.