Sulfur dioxide (SO2) kills by combining with water (H2O) to form sulfuric acid (H2SO4), which, incidentally, is a major component of acid rain (along with nitric acid).
Remember that humans are just great bags of water walking around. When the SO2 touches us, it can't help but find water. You inhale it, there's moisture in the air and in your lungs, you get acid directlyin your lungs. Similar with your eyes, nasal passages, trachea, and so on. Depending on the SO2 concentration, it can cause severe acidic tissue burns, acute pulmonary edema (which is an uncontrollable "leaking" of bodily fluids from damaged surfaces), or death.