The main benefit of a pedal kayak is not having to use paddles. This can be good and bad. You can definitely move fast by not using paddles, but steering can be a little more difficult until you get used to it. By changing from paddles to pedals, you swap maneuverability for speed.
Pedal kayaks are most commonly used for fishing since you can take your focus off of paddling and concentrate on your fishing instead. Legs are stronger and have more stamina than arms, so it just makes sense to utilize them to propel your kayak. However, pedal kayaks are mostly recommended for fisherman. Most others enjoy the paddling process that goes along with traditional kayaks.