To be watchful is to be alert and aware. A watchful dog might keep an eye on the sidewalk in front of your house all afternoon.
The adjective watchful is good for describing someone who keeps an attentive eye on things. A watchful teacher, for example, knows immediately when a student is being teased, and a watchful driver is quick to stop for a pedestrian crossing the street. When you're on the lookout, you're being watchful. The word comes from the Middle English waccheful, which used to have an alternate meaning of "wakeful" or "sleepless."