Baking soda (NaHCO3) is the friendly household name for sodium bicarbonate or bicarbonate of soda, and it's a very useful substance. It's used as a leavener in baked goods, as a cleaner, a deodorizer, and as an antacid.
Baking soda is often used to leaven muffins because, when it is combined with an acidic ingredient such as buttermilk, yogurt, or molasses, produces carbon dioxide gas bubbles, which causes a batter to rise. This reaction occurs immediately once baking soda is moistened with an acid, and so baking soda should be mixed in with the other dry ingredients first, then the liquid ingredients should then be added, mixed quickly, and placed into the oven right away.
Baking soda is also a non-toxic, environmentally friendly cleaner. Sprinkle it onto tubs, counters, and the like, rub, and rinse well to avoid leaving a residue. An open container of baking soda will absorb odours in a fridge. If you have a clogged drain, pour some baking soda down it, follow with some white vinegar. The combination of baking soda and vinegar, by the way, makes an exciting fizz in any context, and so can be used to simulate an explosion, if it takes your fancy.
Alka Seltzer, Eno, and the like - those fizzy tablets that you drop in water and drink when you have an upset stomach - are made from something like baking soda, and you can use baking soda for this if you need an aid against indigestion and don't have those medicines. It tastes disgusting, though.