Ugh… HowStuffWorks didn’t really explain much of anything at all (at least based on the first few articles that turned up on a search for “sneeze”).
Wikipedia, on the other hand, had all kinds of interesting things to say, like:
Sneezing typically occurs when foreign particles or sufficient external stimulants pass through the nasal hairs to reach the nasal mucosa. This triggers the release of histamines, which irritate the nerve cells in the nose, resulting in signals being sent to the brain to initiate the sneeze through the trigeminal nerve network. The brain then relates this initial signal, activates the pharyngeal and tracheal muscles and creates a large opening of the nasal cavity, resulting in a powerful release of air and bioparticles. The reason behind the particularly powerful nature of a sneeze is attributed to its involvement of not simply the nose and mouth, but numerous organs of the upper body – it is a reflectory response that involves the muscles of the face, throat, and chest.
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(The italicized text is to explain “what’s going on” and the bold text explains why your nose tingles.)