The fizzing you see when you drop an Alka-Seltzer tablet in water is the same sort of fizzing that you see from baking powder. If you look at the Question of the Day on baking powder, you will find that the baking powder reaction is caused by an acid reacting with baking soda (sodium bicarbonate). In school, you probably tried an experiment where you mixed baking soda with vinegar to see it foam. That's what is happening in baking powder.
If you look at the ingredients for Alka-Seltzer, you will find that it contains citric acid and sodium bicarbonate (baking soda). When you drop the tablet in water, the acid and the baking soda react -- this produces the fizz. You can think of an Alka-Seltzer tablet as compressed baking powder with a little aspirin mixed in.
Here are some interesting links: