Spine or longeron

A spine is a vertical stick, usually going from the front (top) to the back (bottom) of the kite. It is marked with red on the illustrations below. Some kites may have more than one spine. F.ex. the Tunnel delta kite and the Genki kite

Spines can be made from carbon-fibre, glass-fibre, bamboo or wood. They can be round, square, flat and probably any other shape you can imagine. If you choose to use wood or bamboo it is important that the sticks are as straight as possible and the weight evenly distributed. This not a problem with carbon-fibre and glass-fibre. Other important factors to consider may be stiffness, strength and total weight. 

You can often find that spines are simply called sticks or spars. On Box kites they are called longerons. On the tunnel delta kite below, the two sticks in line with the sail are longerons while the one at the bottom of the tunnel is the spine. 

The term longeron is well worth checking out on Wikipedia. I learned a lot of stuff I didn't know previously.