Unlike pneumonia, in which the whole of the lungs are involved, bronchitis only affects the upper part of your respiratory system. It is an inflammation of the lining of the bronchial tubes, as Webby says. When the bronchi are inflamed and/or infected, airflow to and from the lungs is restricted.
Inflammation may be caused by a virus, bacteria, smoking or inhaling pollutants or dust. As a result the cells of the bronchial-lining tissue are irritated. The cilia (which trap and eliminate pollutants) stop functioning, and air passages become clogged by debris and irritation increases. In response, a heavy mucus or phlegm is secreted and usually coughed up. This is pretty darn gross, as you might imagine.
Acute bronchitis can be associated with severe colds or flu. Getting better requires rest and lots of fluids. You can also take cough medicine that contains an expectorant which will liquify the phlegm so you can spit it up more easily. This impresses friends, lovers and colleagues to no end. But if you don't get over it and it spreads, you can get Broncho-pneumonia and then you're in for a long and nasty illness.
Chronic bronchitis is usually caused by damage due to smoking, but can also be a reaction to too many attacks of acute bronchitis. Chronic bronchitis features seasonal or continual attacks of bronchitis, or the infamous smoker's cough or other incredibly evil coughs.