That's not an idiom. Keeping a matter secret means not letting anyone know about it.
It means you have a guilty secret. Just imagine if you had a dead body in your closet. You wouldn't want anyone to know it. If someone has a 'skeleton in their closet' it means that they have a secret from their past that they are hiding. a shameful and shocking secret that people try to keep hidden
don't reveal a secret
It means things which occur in secret.
This is not an idiom - it means exactly what it says. You should stay fit and healthy.
It is just an idiom and has no history.
Keep it under your hat. Play your cards close to your chest. Don't let the cat out of the bag.
keep it under the hat
The idiom "keep an eye out for" refers to watching for something or someone. An example of a sentence using the idiom would be: Jeff should be arriving soon, so keep an eye out for him.
Keep watch on.
It means you have a guilty secret. Just imagine if you had a dead body in your closet. You wouldn't want anyone to know it. If someone has a 'skeleton in their closet' it means that they have a secret from their past that they are hiding. a shameful and shocking secret that people try to keep hidden
don't reveal a secret
To get to the point.
It means things which occur in secret.
This is not an idiom - it means exactly what it says. You should stay fit and healthy.
Obviously, you can't keep the letter as it would explode. This does not matter because you still get the stamp for it.
It is just an idiom and has no history.
You could say they "stick to it," or "keep at it."