A situation in which a person either hides or downplays some aspect of themselves because they do not want to feel (or have others feel) uncomfortable [Deloitte]
My manager made it clear that a physical condition he had (that was largely invisible to everyone else) would at times affect his ability to work long hours late at night. Him disclosing this, instead of toughing it out or making up excuses, allowed the entire team to be more honest with our own individual challenges, which I really do believe helped us do better work in the long term.
At my consulting firm, a male Senior Manager told us a story about how he would tell coworkers he had "important weekly client meetings," but he was actually spending time with his kids. He was trying to "cover" because he believed other men would not understand why he would need to spend time with his kids during the week – he thought other men would judge him and think this responsibility fell on his wife.
Facts and Data
Some forms of covering are a part of doing business while others are more harmful. HBR writes: “Enabling employees to feel comfortable being themselves could unlock dramatic performance gains because they can focus their attention on work, rather than hiding parts of themselves.”
Share your story and be a bit more vulnerable (in the right context)
Know that many people feel it necessary to hide parts of themselves, especially related to their sexual orientation, disability, gender, race, and more.
Don't pressure others to "uncover" anything they don't want to. Just because you might be a safe person to "uncover" with doesn't mean that others are as well.