The prevailing Miasma Theory was that cholera was caused by airborne transmission of poisonous vapors from foul smells due to poor sanitation.
I find it interesting that even though this theory was wrong it should have also improved conditions where those with a strong enough immune system may not have been effected or effected as badly. It seems like a good start but impressive of Dr. Snow to conclude that the method of transmission was different which in turn completely changes the type of sanitation preformed / actions taken to prevent disease.