A Dodge is the act of avoiding taking damage through a special maneuver that grants the dodger temporary intangibility. It is distinct from Guarding in that a guarding entity is still hit, even if the damage is mitigated or nullified.
The ability for Kirby to dodge debuted in Kirby: Triple Deluxe, and has persisted in every main series Kirby title since. It is performed by the player pressing a direction on the + Control Pad (or Circle Pad) while Kirby is Guarding (or just activating a Guard in mid-air). This will cause him to either roll in a certain direction, dodge in place, or dodge in mid-air depending on where he is and which direction was pressed. When rolling, Kirby will move a small amount in the specified direction. When air-dodging, Kirby will not fall until the dodge concludes.
Dodging causes Kirby to be intangible for a short moment (less than a second), which will allow him to avoid attacks that even a Guard could not stop. He is left vulnerable for a short while after the dodge finishes however, so timing is essential.
In Kirby Fighters (and Deluxe), Team Kirby Clash (and its expanded releases) and Kirby Star Allies, doing a rolling dodge will cause the fighter Kirby to move a much greater distance than in the main series, making it match up more closely with the Super Smash Bros. dodge.
In Super Smash Bros.
The act of dodging out of Shield has been a crucial technique in every game in the series, with side-stepping and air-dodging introduced in Melee. Much like in the Kirby series, fighters are intangible for a short period of time while they dodge, and vulnerable for a short time in-between dodges. The dodging techniques introduced in Triple Deluxe were taken directly from the Smash Bros. series.