The GlobalFlyer is flying to the East to take advantage of the jet stream. The jet stream is a core of fast streaming wind that generally flows from West to East. By flying in and near the jet stream, Steve can add to his ground speed. Although he moves through the air at a constant rate, because the air in the jet stream is moving with him also, his speed across the ground can be greatly increased. A simplified view of this effect is that the wind in the jet stream is in a sense "pushing" Steve along. This can greatly increase fuel efficiency, in relation to distance covered over the ground, which allows Steve to fly such a long distance on so little fuel. The jet stream can reach upwards of 200 miles per hour at times.
Example: If you are flying in an airplane at 200 miles per hour, and the wind is pushing you from behind at 100 miles per hour, then your groundspeed would be 300 miles per hour.
The converse is true also. If you are flying in your airplane at 200 miles per hour, and the wind is blowing at you from the front at 100 miles per hour, then your groundspeed would be only 100 miles per hour.
When you grasp the concept of airspeed versus groundspeed, it becomes easy to understand why Steve is flying to the East.