Quite simply, a severe weather watch indicates potential risk for severe weather. A warning means that severe weather has either been spotted on radar or by a spotter within that specific area.
Here are the technical definitions, according to the National Weather Service:
Watch: A watch is issued when the risk of a hazardous weather or hydrologic event has increased significantly, but its occurrence, location, and/or timing is still uncertain. It is intended to provide enough lead time so that those who need to set their plans in motion can do so.
Warning: A warning is issued when a hazardous weather or hydrologic event is occurring, is imminent, or has a very high probability of occurring. A warning is used for conditions posing a threat to life or property.
For additional weather terminology information, you may visit http://w1.weather.gov/glossary/