Nitrous is a gas (N2O). It was discovered in 1772, it is colorless, heavier than air. Dentists and hospitals for anesthesia use it, its nickname is laughing gas. The first use as a motor fuel was during World War 2, after which it was forgotten until 1962. It is injected, together with fuel, in to the engine, and produces a considered amount of power, the amount being proportional to the fuel and nitrous injection. Simple! It works in the engine in 3 ways:
1) It releases free oxygen, which burns your fuel mixture better.
2) It cools down the air, which increases the density. You get more gas in to the cylinder.
3) It releases a large amount of heat, when the nitrogen is split from the oxygen above 300 degree C.
Nitrous (and fuel) is applied to the engine via a solenoid, which is activated by an electrical signal from the dashboard or other means. The result is the same: You get an instant power boost, you may loose traction, and worst case, hit the rails! It is very impressive!

Latest technology employs a controller, which gradually (progressive) applies the nitrous and fuel mixture under pre-programmed engine operating conditions. It is even possible to limit the power to a safe level by limiting the amount of nitrous and fuel. This technology allows an otherwise racing "gimmick" to be employed in normal street use. By anyone! Apart from applying the nitrous, the controller also de-applies it before you hit the rev-limit, which may have a disastrous effect otherwise.

When do you use nitrous? In short sprints, during acceleration, overtaking and dicing. It is a safe technology, used for many years.