Curiosity piqued by something mysterious or puzzling.
Curiosity piqued by something mysterious or puzzling; also (separately) a secret scheme or plot.
As an emotion, curiosity specifically piqued by the mysterious, puzzling, or partly hidden — it needs an enigmatic trigger, a sense of more beneath the surface. Sharper than plain interest and more momentary than the absorbing fascination; all intrigue is a form of curiosity, but curiosity needn't involve mystery. Most natural in the passive (“I was intrigued,” “an intriguing question”). Note the separate, non-emotional noun sense “a secret plot.”
Curiosity excited by something mysterious or puzzling.
A late development — the “excite curiosity” sense is from 1894, labeled by the OED a “modern gallicism.”
A secret plot or underhanded maneuvering (“political intrigue”); dated, a clandestine love affair.
The older noun sense, from the 1640s; not an emotion.
From Latin intricare “to entangle, perplex,” via Italian intrigare and French intriguer. The verb entered English in the 1610s meaning “to trick, cheat”; the noun (1640s) meant “a clandestine plot.”
The emotional sense is a late overlay: the verb meant “to trick” (1610s), then “to plot” (1714), and only “to excite curiosity” by 1894 (the OED calls it a “modern gallicism”); “intriguing” (exciting curiosity) is from 1909. No reliable shift more recent than the early 20th century.