The meaning of watch

I'm on my way to Atlanta to give a talk. The flight is overbooked and the United representatives are asking for volunteers to leave with a later flight. I can't do it because my schedule for the day is pretty much fixed. A young couple with a small baby in a stroller are debating if they should volunteer. I can hear that they both have strong Indian accents. The husband goes to ask for some information and the woman explains to me that they are going to Atlanta in vacation so it does not matter but still they don't want to wait too long because of the baby.
A woman with a small boy in tow is walking past us. The boy is about 5 years old. He is carrying a large backpack almost his size.
The woman turns to him and orders him "Please watch the baby". The voice is sharp and strong. The little boy obeys her in a way she probably didn't anticipated. He literally watches the baby and starts walking slowly to keep his eyes on the baby all the time. His mother turns and he follows with his small body twisted to keep looking at the baby. His mother yanks him and pushes him forward.
He probably never knew what he had done wrong.