KEEP YOUR EYES ON vs. KEEP AN EYE ON 見つめる vs. 見張る

To keep your eyes on something is to continue to look at it.

To keep an eye on something is to watch so that it is not stolen, harmed, etc.
keep your eyes on　は、何かを見続ける、つまり、見つめる、という意味です。

keep an eye on　は、盗まれたり傷つけられたりしないように、何かから目を離さないでいる、つまり、見張るという意味です。

(two people driving in the country)
Driver: Oh look! There's a deer over there in the trees!
Passenger: Keep your eyes on the road! I don't want to get into an accident.
(a baseball coach to one of his players)
Keep your eyes on the ball when you're batting.
(a teacher to her students before a test)
Remember to keep your eyes on your own paper at all times. Anyone caught copying answers will get a failing grade.
(waiting at an airport departure gate)
Would you keep an eye on my suitcase for me? I need to go to the restroom.
The doctor found a dark mole on my back. He said it's probably nothing, but that I should keep an eye on it in case it gets any bigger.
(a friendly neighbor)
If you ever need someone to keep an eye on the kids while you do an errand, just give me a call.

Be sure to keep an eye on your mailbox, because we'll be back in no time!