I would like to complement ailie for the awsome write-up of what asthma is. However there is one thing I would like to add: treatment.

Asthma is something that tends to be taken lightly, especially by school officials. However this is wrong, as an asthma attack can kill a person. If a person seeks you out when they are having trouble breathing, they have a reason to. Most asthmatics I know (and myself) are very self-reliant. They don't ask for help unless they need it, or might need it. If the person is wheezing, uses a fast acting inhaler, and doesn't improve, or gets worse, the next step is 911, unless they say otherwise. If the person has had the wind knocked out of them, help them up, give them something to lean on. They will lean hard, if you personally can't support the weight, don't let them lean on you. If they start hyperventilating, deep breathing is probably the best method for getting the attack under control.

Don't Panic
As corny as that sounds from a Douglas Adams generation, it will only make the attack worse
Remember, asthma is not just lungs constricting, it is depriving the brain of valuable oxygen. Many get extremely light-headed, dizzy, and disoriented when having an attack. You may, or may not, hear wheezing. Never, never, hug an asthmatic who is having an attack, or place any weight on them. When hugging a known asthmatic, if they start pushing out with their arms, or otherwise try to get away, let go -- they have a reason. If you can, take their backpack/purse off, but do it slowly -- remember, fast motions at a person can have bad effects if they can't think straight. Let them see where you place it, make eye contact with them. You can learn a lot about a person's train of thought when you can see their eyes, and they can read the same from you.