A "watch" means that conditions are right for the event to happen. So, for example, if we say there's a "High Wind Watch" for an area, that means that high winds are possible, but not imminent. It's an early heads up that something merits close attention.
A "warning" means the condition is imminent or already happening. Thus, a "High Wind Warning" means that high winds are happening now, or are going to happen in the warning area.