Plausible deniability is a term coined by the CIA during the Kennedy administration to describe the withholding of information from senior officials in order to protect them from repercussions in the event that illegal or unpopular activities by the CIA became public knowledge.
The term most often refers to the denial of blame in (formal or informal) chains of command, where senior figures assign responsibility to the lower ranks, and records of instructions given do not exist or are inaccessible, meaning independent confirmation of responsibility for the action is nearly impossible. In the case that illegal or otherwise disreputable and unpopular activities become public, high-ranking officials may deny any awareness of such act or any connection to the agents used to carry out such acts. It typically implies forethought, such as intentionally setting up the conditions to plausibly avoid responsibility for one's (future) actions or knowledge.
In politics and espionage, deniability refers to the ability of a "powerful player" or intelligence agency to avoid "blowback" by secretly arranging for an action to be taken on their behalf by a third party ostensibly unconnected with the major player. In political campaigns, plausible deniability enables candidates to stay "clean" and denounce third-party advertisements that use unethical approaches or potentially libellous innuendo.