Inflammation that airways (bronchial tubes) swollen and sensitive is the main factor that causes them to narrow. Inflamed bronchial tubes result in a smaller space for air to pass through. In addition, the muscles surrounding the airways may tighten, further narrowing the space for airflow.
When the airways react they can also produce more mucus, which is a sticky and thick liquid substance that can clump together and even further narrow air passages. On top of that certain allergy and inflammation cells (eosinophils and white blood cells) accumulate at the site of the inflammation, causing tissue damage and even further narrowing airways.
This chain reaction can result in difficulty breathing and asthma symptoms.