On the watch (for someone or something) American British informal
If you ask someone to be on the watch for (someone or something), you mean that he has to look out for someone or something carefully and actively.
My mom always tells me to be on the watch for pickpocket on the bus.
If you come back home in the middle night, please be on the watch for robbers on the streets.
The doctors were always on the watch for early symptoms of the disease.
To observe one's activity
Protect one from harm caused by unforeseen events
To concentrate on minor details instead of the whole situation.
To watch someone or something very closely and carefully
To pay close attention to someone or something.