An open secret is a concept or idea (often in, but not necessarily limited to, government and military circles) that is "officially" secret or restricted in knowledge, but is actually widely known; or refers to something which is widely known to be true, but which none of the people most intimately concerned is willing to categorically acknowledge in public.
Examples of military open secrets:
An example of open secret in politics: it may be widely known that an individual government minister holds a particular opinion, but is at present unable to express that opinion publicly because it is contrary to the formally expressed view of the government of which he or she is a member.
The book Cat's Cradle by Kurt Vonnegut, Jr. includes the religion of Bokononism, outlawed in the fictional San Lorenzo. There are severe punishments for anyone found to be a practitioner of this religion. The open secret is that while everyone in San Lorenzo denies being a Bokononist, they all are. This includes even the dictator of the island, by whose command it was outlawed.
The term has also been applied to public knowledge of a person's sexual orientation. For example, the composer Benjamin Britten was homosexual, but never identified himself as such. Nevertheless, it was widely known and was thus an open secret.