Crouching, often simply called ducking, is a ground-based position achieved by holding down on the Control Stick when standing. Crouching shortens the character's damageable collision bubble and can be used to crouch cancel enemy attacks. A crouching character can also crawl, if the character has the ability.
How well a crouch can help a character dodge attacks is highly dependant on the crouching animation. Some characters can become very difficult to hit since they crouch so low (such as Kirby, Jigglypuff, Snake, and Sheik, Mr. Game and Watch). Other characters, however, barely lower themselves at all by crouching (such as Meta Knight and Bowser).
Dedede's crouching animation is unique in that he lays down in a lazy pose, the only crouch that can be used as a sort of fourth taunt.