In political and intelligence discourse, this means that an event cannot conclusively be traced to the party who ordered it. The event may be a coup, assassination, cover-up or the like, committed by some middleman or proxy.
Even if a connection can later be demonstrated, the public may still resist the information because the original lie is more plausible, i.e. better fits their pre-existing ideas of how things should be.
For example, maintaining plausible deniability is important when mounting a false flag operation. Such a thing is for example an attack on one's own people, blamed on one's enemy of choice, for the purpose of justifying aggression.