The phrase implies continuous attention and watchfulness over a period. Can you keep an eye on the pot to make sure it doesn't boil over?
Pro Tip 2/3
Not Literal
It's a figurative expression meaning to be attentive, not to literally watch something non-stop. I'll keep an eye on the news for any updates about the event.
Pro Tip 3/3
Caution Implied
Using this phrase often suggests that there might be a risk or issue to be aware of. Keep an eye on your belongings in crowded areas to avoid theft.