According to the Cleveland Clinic web site, "Antihistamines help relieve symptoms by blocking the action of histamine. Histamine is a naturally occurring substance that is released by the immune system after being exposed to an allergen. When you inhale an allergen, mast cells located in the nose and sinus membranes release histamine. Histamine then attaches to receptors on nearby blood vessels, causing them to enlarge (dilate). Histamine also binds to other receptors located in nasal tissues, causing redness, swelling, itching, and changes in the secretions. By blocking histamine receptors, antihistamines prevent symptoms" (Cleveland Clinic web site 11/10/2008).
So in essence what is occurring is an antihistamine blocks the ability of the body's histamine to attach to the normal receptor to tell the body to have a runny nose, itchy eyes, swelling, etc. They do not inhibit the release of histamine, as this would affect a wide array of other vital body functions that rely on histamine to work properly (such as acid production in the stomach).