Plausible deniability involves the creation of power structures and chains of command loose and informal enough to be denied if necessary. The idea was that the CIA (and, later, other bodies) could be given controversial instructions by powerful figures -- up to and including the president himself -- but that the existence and true source of those instructions could be denied if necessary; if, for example, an operation went disastrously wrong and it was necessary for the administration to disclaim responsibility.
The doctrine had two major flaws. First, it was an open door to the abuse of authority; it required that the bodies in question could be said to have acted independently, which in the end was tantamount to giving them license to act independently. Second, it rarely worked when invoked; the denials made were rarely plausible and were generally seen through by both the media and the populace. One aspect of the Watergate crisis is the repeated failure of the doctrine of plausible deniability, which the administration repeatedly attempted to use to stop the scandal affecting President Nixon and his aides.