Merits can be public or hidden. When you hide a Merit, it can no longer be viewed on your profile by other people. The exception is for an Admin from the Org that sent you the Merit. They can view this hidden Merit even if it is hidden, because they sent it to you. Hidden Merits also cannot be shared to social media. You can make a Merit hidden by clicking "Hide Merit" in the menu of one of your Merit's pop-up windows.
Permanently Hidden Merits are sometimes created by Orgs. Permanently hidden Merits function the same was as normally hidden Merits, but they can't be unhidden by you.