You release the oxygen in sodium chlorate by heating it. When you heat nitrous oxide to about 570 degrees F, it splits into oxygen and nitrogen. The injection of nitrous oxide into an engine therefore means that more oxygen is available during combustion. Because you have more oxygen you can also inject more fuel, and that means the same engine can produce more power. Nitrous oxide is one of the simplest ways to provide a significant horsepower boost to any gasoline engine.
Nitrous oxide has another effect that improves performance even more.
When it vaporizes, nitrous oxide provides a significant cooling effect on the intake air. When you reduce the intake air temperature you increase the air's density, and this provides even more oxygen inside the cylinder. The only problem with nitrous oxide is that it is fairly bulky and the engine needs a lot of it. Like any gas it takes up a fair amount of space even when compressed into a liquid. Therefore a car normally carries only a few minutes of nitrous oxide and the driver uses it very selectively by pushing a button.