Common theory is that it forces the two hemispheres to become less independent-- by having one side constantly be forced to monitor and work with the other, it somewhat forces the two regions to collaborate. Ultimately the co-operation allows for better efficiency and survival then two competing centers. A similar argument from Holtzmann (Cornel): He posited that working on one kind of task uses certain brain resources; the harder the task, the more of these resources are needed - and the more one half of the brain must call on the subcortex or the other hemisphere for help. In 1982 Holtzman led the way again, discovering that, indeed, the harder one half of a split brain worked, the harder it was for the other half to carry out another task simultaneously. More corroboration-- In what must have been fierce competition for cortical space, the evolving primate brain would have been hard-pressed to gain new faculties without losing old one. Lateralization could have been its salvation. Because the two hemisphere are connected, mutational tinkering with a homologous cortical region could give rise to a new function - yet not cost the animal, because the other side would remain unaffected (Gazzata, Dartmouth).
The physical reason is that the nerves cross over each other inside the brain, and nerves on the right side of the brain cross to run down the left side of the body, etc. Nobody really knows exactly why this evolved.