A condition in which a subject can safely and believeably deny knowledge of any particular truth that may exist because the subject is deliberately made unaware of said truth so as to benefit or shield the subject from any responsibility associated through the knowledge of such truth.
The CIA black ops division undertakes dangerous and usually what would be considered illegal missions that are not officially sanctioned by the US administration so that the administration, which usually benefits from such missions, can safely dissavow any knowledge of them in the event of their publically uncovered success or failure. The administration is in the position of plausible deniability towards the CIA's actions.
Plausible deniability actually is a legal concept. It refers to lack of evidence proving a allegation. Standards of of proof vary in civil and criminal cases. In civil cases, the standard of proof is "more likely so than not" whereas in a criminal matter, the standard is "beyond a reasonable doubt" If your opponent lacks incontrovertible proof (evidence) of their allegation, you can "plausibly deny" the allegation even though it may be true.
Because many lawyers are in politics, they brought this lower standard of ethics and integrity with them. This is why they rarely put anything controversial in writing. This is also why they most often have you talk to an underling or an agency bureaucrat so they can plausibly deny knowledge of the conversation or be able to say the underling or bureaucrat misstated their position.
Before the blue, stained dress was found, Bill Clinton's position was plausible deniability with regards to having sex with that woman.
When it is acceptable for a party to lie about what they did because the truth would hurt too much and cause many problems.
Plausible deniability is a larger version of a white lie.