'Rage' is a mechanic introduced in Super Smash Bros 4. The name comes from how highly damaged player are emitting smoke (and thus 'raging'); however, the mechanic is present even below 100% when no smoke is visible..
In Super Smash Bros. 4, a player with higher damage deals slightly higher knockback than when their damage is low. This does not affect damage dealt. It is currently unclear how significantly rage affects the amount of damage necessary to KO an opponent.Source: