The experiment is built on the idea that some chemical reactions create gas as a product (an outcome) of the reaction. If a gas generating reaction is carried out in an enclosed space, the result can be dramatic, as we saw on television. Doing this experiment is not very hard, but because something gets shot out of the bottle, it is important that safety be the first thing to be considered. Never shoot a bottle made for this experiment at somebody...even if the cork or stopper doesn't move very fast it may have small amounts of chemicals on it and though the chemicals used are relatively safe, any chemical in a persons eye, for example, could cause serious injuries.
The chemical name of baking soda is sodium bicarbonate. The bicarbonate part of this chemical is the important part that makes the reaction happen. It is an example of a base, which can react with an acid. When it reacts with an acid, carbon dioxide gas is generated. Citric acid is the chemical that provides the acid, but when it is a solid the part that makes it an acid cannot get "free" to react. By adding the water (from the straw) when the bottle is tipped upside down the reactive part of the citric acid (a hydrogen ion - present in all common acids) reaches the bicarbonate part of the baking soda and the reaction quickly generates the gas - causing the top to pop off.
Links
What is Cork? - if your stopper is cork, you might wonder what it is...
What is rubber - if your stopper is rubber this page can help you know how rubber is made.
Science supplies on line - if you need to buy science supplies over the net there are a few places - here's one.