People who chew with their mouths open often aggravate the people near them, meaning that they exasperate their neighbors.
One trick for remembering the meaning of aggravate is to recall that it rhymes with one of its synonyms, irritate. When you irritate, you aggravate. Younger brothers often aggravate their older brothers, because they find it entertaining to get a reaction out of them. Aggravate is also used is to mean "make worse." For example, if you have an old knee injury, it's probably best not to climb Mount Everest, because you might aggravate the injury. If your house is in foreclosure, calling your banker an ugly name is likely only to aggravate the situation. Try a little sweet talk instead!