What geological theory explains how llamas and camels, close relatives, might be found on different sides of the world?

The answer is continental drift. 
Continental drift is the geological theory that explains how continents move through Earth's surface. All continents were once connected as one supercontinent Pangea. On that supercontinent, many related species, such as llamas and camels, lived together on one location. But after continents spread apart, related species were separated on different continents and adapted to different conditions