It is usually used in reference to some celebrity or well-known person. It is very seldom used concerning people we work with or acquaintances.
"The politician resigned when it was found he had a skeleton in his closet - multiple convictions for drunk driving, some of which were recent."
"He will be appointed commissioner by the mayor, following a background check for any skeletons in his closet."
Quote from Burt Reynolds (famous actor):
"I could never go into politics. I don't just have skeletons in my closet - I have bodies!"