The Latin word plausibilis means "deserving applause, acceptable", and this morphed into our English word plausible with the meaning, "having the appearance of truth", first used around 1560.
Merriam-Webster defines plausible as:
- superficially fair, reasonable, or valuable but often specious
- superficially pleasing or persuasive
- appearing worthy of belief
"Plausible deniability" is often used in intelligence work: in false flag operations, active measures, offensive cyber ops, anti-terrorism in denied countries--we did not do it, and my boss especially does not know anything about it.
In cryptography it can mean deception about the presence of a message--while having a reasonable explanation. Alice can deceive you about a chunk of data, and you will not know for sure whether plaintext is or is not there--it will take work to figure out the truth, but even after you prove that Alice deceived you, she can still make a case that is believable... or say I did not know....
"Plausible deniability" can also apply to hiding an encrypted volume in a storage device and then denying its existence. Veracrypt is a good example of a product that can offer plausible deniability: this USB does not contain a hidden, highly encrypted volume, enciphered with a cascade of TWOFISH/AES256 hashed with Whirlpool.
With internet protocols it means that two parties can deny having taken part in key exchange. This might seem to be an odd virtue in key exchange. In fact, this kind of deniability is an important feature.
You can read more about this last topic here.