Believe it or not, asthma is a disease of air trapping.  What happens is air comes in, the airways constrict and swell, and air gets trapped in the lungs.  While it may feel as though you can't get air in, the reality is you can't get air out.  In fact, this air trapping is one of the reasons that during an asthma attack it often feels like you can only take in half a breath, or a quarter of a breath. 

This air trapping is also one of the reasons that diaphragmatic breathing is a technique often taught to asthma and COPD patients. The idea is if you give your lungs more time to exhale some more air might escape your clamped down air passages.  Of course you probably know your rescue inhaler also works to relax your air passages to, thus letting out this trapped air.