They consist of a smooth tire core which has a series of large rubber cups (or paddles) attached to it.
Street legal mud tires are a compromise between large voids and a smooth rolling shape for on-road use.
[1] The more "extreme" a mud tire (such as a "Super Swamper") is, the harsher and louder it is on a hard surface.
This means that it is used on a wheel that drives a vehicle to push it forward, but gives little "lateral" (side-to-side) traction.
Paddle tires are available for motocross bikes, all-terrain vehicles, sandrails, and 4 wheel drives.