Here's a breakdown:
* Conspiracy: A secret plan by a group of people to do something illegal or harmful.
* Conspiratorially: Describes an action, tone of voice, or look that implies involvement in a conspiracy.
Example:
"They looked at each other conspiratorially, their whispers barely audible above the music."
This sentence implies that the people are sharing a secret or planning something together in a way that is meant to be hidden from others.