The body is a very sophisticated machine so there are obviously some extremely complicated things going on inside when a person hyperventilates. Basically, what happens when you hyperventilate is that you start breathing excessively fast. In other words, you begin to take in more oxygen than your body generally needs.
This hyperventilation or rapid breathing can be caused by any number of things but is often associated with stress and anxiety. If you are in a situation that you deem to be very stressful, your body might respond by breathing heavily. A good example that comes to mind is someone who decides to parachute from a plane for the first time or someone faced with a dangerous situation like an attacking animal or robber.
Hyperventilation is normal for many people as their stress level goes up. Breathing can become very difficult as the body tries to rebalance and this can lead to dizziness and other panic attack type symptoms.
Once the body detects an imbalance of oxygen and carbon dioxide in the system, the result is hyperventilation in an attempt to bring everything back into balance. Sometimes a brown paper bag was used to speed up this process.
Paper bags were often used in the past as a method to introduce more carbon dioxide back into your system and hopefully stop panic attacks. However, many experts today disagree with using this method.
You can often help someone who is hyperventilating by getting them to count between breaths while trying to slow down their breathing. It's a good idea to calmly talk with them and try to get them to relax.