What causes watery eyes and a runny nose?

Almost anything. Triggers can basically be divided into allergens and irritants. Allergens will include pollen from trees, weeds, and grasses. Also mold, dust mites and pets. Irritants include dust, smoke, cleaning products, changes in weather, etc. The are other rare causes of these like migraines.
Enviroment Allergies. 'tis the season with everything bloming to have 'environmental allergy symptoms' of watery eyes, runny nose. Daily anti-histamines are available otc (zyrtec, claritin, allegra) and may help with symtoms. You may want to get seen if not improving. A prescription of Flonase nasal spray (fluticazone generic) may help or a trial of singulair (montelukast). An allergist can be a great resource.