Handles: used to control a foil kite in replacement of a control bar. In 4 line kites, two curved handles are used. One side (top) of each handle hooks to a power line connected to the main bridle of the kite on one side. These lines control the steering and hold the down the power of the kite. One brake line connected to the bottom of each handle runs along to a smaller bridle on the trailing edge of the kite. This allows the kite to be stalled or braked. A "link line" or harness line runs between the two handles to allow a harness to take the load of the kite and for one-hand or short-term no-hands flying. These can allow for more precise landing, better luff recovery, quicker handling and better sensitivity, but less tendency to automatically return to a neutral position, less solid-feeling, more "fumbly" and usually twitchier. Not used with inflatable kites.
Hangtime (Airtime): the amount of time spent in the air while jumping.
Hard rails, soft rails: The rounder the edge of the board the softer the rails are said to be. Hard rails means a sharper edge and allow better upwind performance.
Harness: worn by kite pilot around the waist or hips to transfer the energy of the kite to the body and remove the load from the arms. It has a hook in the front known as the Spreader Bar. The chicken loop hooks into the spreader bar allowing the kite power to be adjusted on the fly. Similar to a windsurfers harness but usually consisting of a handle or line around the back for the kite leash to attach to.
Heelside: the side of a board on the edge where your heels are (opposite of toeside). To ride heelside down is normal.
Hooked in: the act of being connected to the harness through the chicken loop to the spreader bar.