Always be alert. Stay aware.
If you are a guard and you are guarding something valuable, you cannot sleep. If ya sleep, somebody steals it.
As an idiom, its meaning is broader, but it still means “don’t let something out of your sight” or “never become unaware of potential threats”
Sleeping with “one eye open” means you are either spying for when someone comes home, or pretending to sleep to eavesdrop on a conversation, or you are afraid that someone is gonna get you or steal from you if you fall asleep.
it’s “open” not “opened”.
The other answers are very good though, each adding a different sense.
If your are the parent of a small child, you have probably learned this ability.
If not, you may awake one morning to find all of the walls in you house decorated to chest high by crayon drawings.
well in my experience i sleep with one eye open when i m scared cause i can t sleep thinking theres someone watching me ( a ghost ) so i keep my one eye open to see if theres a ghost around me or what..
It’s called unihemispheric slow-wave sleep (USWS), and it allows birds to detect approaching predators while still getting a bit of shut-eye.
“They are able to make behavioral decisions about whether they keep one half of the brain awake or allow both halves of it to sleep,” Niles Rattenborg said in a telephone interview.
To always be on your guard.
watch your back