Kiteboarding (or kitesurfing) combines windsurfing, surfing and wakeboarding techniques. You balance and on a board and hold a bar which is attached by two cords to a ribbed kite. The kite enables you to move and jump in the wind. The bigger the kite, the lighter the wind you can go in and vice versa.
The only place I know where you can go kiteboarding (unless you are carrying all the equipment with you) is at Santa Marianita beach near Manta. Check out the links below.
Kiteboarding school: www.humboldtkites.com
Kiteboarding info: www.thekitehouse.com