Generally in the context of international affairs, an event has plausible deniability when a nation can assert, with a reasonable chance that its claim will be accepted, that the nation did not cause the event in question. Sometimes, of course, a nation may have had nothing to do with the matter in question, but it may also have indirectly or directly sponsored those who did it.
The term is often used to refer to actions performed by a covert action part of the government. Sometimes, it may have been performed by military or intelligence personnel, but, in either case, there is no direct linkage to the government.
In psychological operations, "black" propaganda is associated with a different country than its actual source. The source of "gray" propaganda is deliberately indeterminate.