http://eclipse.gsfc.nasa.gov/OH/OHres/SEfigurekeyP.html has an explanation of the map.
The far western part (Angola out to the Atlantic) of the figure 8 is where the partial eclipse ends right at sunrise. The curve to the east (Angola to South Africa to Antarctica) is where the eclipse starts at sunrise. The straight line in between is where the eclipse is at its maximum at sunrise. The eastern loop is similar for sunset. They join right where the sun is barely above the horizon at the combined sunrise/sunset in the antarctic winter when the partial eclipse occurs.
http://www.universetoday.com/119241/a-complete-guide-to-the-march-20th-total-solar-eclipse/ discusses the March eclipse with a more detailed graph of that eclipse.
The labels on this image make it really clear what the figure-eight is. It is really sort of like two overlapping curves.
The eclipse made a perfect bull's-eye on the North Pole. Pretty amazing.
click image to make it full size