Riding unhooked unleashes the real power of the kite - and removes your depower, which can be scary. The technique is used for both wave riding and jumping tricks.
Learning to handle the kite unhooked, on the beach:
This same technique applies for unhooking and re-hooking in surf and flat water.
Here is a fantastic video of how to learn to unhook. It comes at it from a surfing angle but the same technique applies.
When surfing "down the line" on a wave, being unhooked with the kite "parked" means it is not generating much pull, and being unhooked frees your body up when surfing and turning the board. You can also fine tune the kite power by pushing your arms out or pulling them in.
When jumping, being unhooked allows your body to rotate and spin free from the kite lines, which facilitates a number of advanced aerial tricks.