Three common causes of a runny nose are allergies, a cold, and a sinus infection.
If you are allergic to something (your allergen) such as tree pollen, your body mistakes that allergen for something harmful to your body. When you come in contact with the allergen, your immune system jumps into action by releasing antibodies and other chemicals to fight off the invader. One of these chemicals known as histamine causes the symptoms we associate with an allergic reaction including itchy or watery eyes and a runny nose.
Allergy symptoms show up after you have been exposed to your allergen. If you get away from the allergen, the symptoms should go away and your nose should stop running. Some allergens, like cat hair, tend to be localized. So if you visit someone with a cat you can expect a runny nose that will clear up when you leave the area.