Asthma is a lung disease that primarily affects the bronchial tubes. It basically causes the airways to constrict, thus causing a difficult breathing situation for the asthma sufferer.
I feel for you man, I've had asthma since I was a kid (I'm 34 now).
Asthma can manifest itself in several ways. It can be environmentally induced (meaning, things in your environment such as allergens, cigarrette smoke, etc. can trigger it and cause an attack). Or, it can be excercise induced - meaning that when you engage in physical activity, you can get an attack. Or... it can unfortunately be both.
Asthma can range from being very mild (meaning some airway constriction and difficulty breathing) to severe - life threatening. If you haven't been to the doctor yet (which it sounds like you have been), I'd encourage you to go ASAP so that you can get tested and get treatment.
Luckily the prognosis can be good. There are a wide variety of medicines that can be taken as well as inhalents which can help an asthma sufferer to lead a relatively productive and active life (that is, if you have moderate to light asthma). Inhalers such as Albuterol (which is what I use) can be used on an "as needed" basis and can stop an attack or even be used preventatively if you are engaging in an activity which is likely to provoke an attack.
There are also a plethora of sites online which can provide you some information if you need it.
I hope that helped a little bit. Yeah, it sucks to have it... but I've been very lucky to lead a very productive life despite my asthma. I can do pretty much anything I want to do... I only have to make sure to have my inhaler with me if it's going to be excessively physical to make sure I don't get an attack. I've been very fortunate that as I've gotten older, my asthma has become much less severe.