Sneeze is designed to show how rapidly the flu can spread from person to person when the appropriate preventative measures are not taken.
You are the virus. You've already infected one person and can cause them to sneeze - but only once per level. The idea is to maximise your sneeze by hitting other people with your revolting green mucus. Once hit, the virus infects them, causing them to sneeze and continuing the chain reaction of snot. There are ten levels and the goal in each is to infect a certain percentage of the population.
Now, please go and wash your hands.