SEATTLE - It travels in both directions, really. In a cloud-to-ground strike, an electric charge from the cloud starts coming down, and gets about 2/3 the way toward the ground.
At that point, a return stroke of opposite charge will race up from the ground and meet the original charge, creating a channel where the electricity can flow back and forth several times until the charges have been neutralized.
So the short answer is that the lightning collides in mid-air between the cloud and ground. However, you can have cloud-to-cloud or cloud-to-air lightning too, so it can really travel in any direction.