Sneezes are not only a forceful expulsion of air in order to clear
irritations but, when having a
cough, it makes sure your
brains will get enough
oxygen to function properly. Aka, a natural reaction of the body trying to keep a healthy
equilibrium. (Btw, cows sneeze at least 7 times as much as humans do...)
Covering your mouth when sneezing is more an act of being polite, but essentially doesn't really matter for the people next to you at all. When you sneeze with your mouth uncovered, the aerosols (with mucus, saliva and the bacteria) can float around in the air up to 10 meters in distance (and become relatively very diluted in the air). If the mouth is covered, it's up to a maximum of about 5 meters, with a higher concentration of the droplets (not the same amount of course, the rest is on your hands).