Intrigue derives from the Latin word "intrigare," which means "to entangle."
Intrigue often entails deception and duplicity, creating a need to parse through the lies and find out the actual facts.
The word often has a romantic association, referring to secret (and usually illicit) liaisons between a given couple. That naturally dovetails into the word's other meanings.
Above all, intrigue entails complexity, using artifice and façade to add twists and turns to plot which may otherwise be straightforward.
Though it's often used as a noun, intrigue can also be used as a verb: one can be "intrigued" by having one's curiosity or interest incited.