Refers to a romantic or amorous relationship, often with a slightly literary or old-fashioned feel. Can imply a secret or passionate affair.
He seems to have had many love affairs when he was young.
The novel depicts a forbidden romance.
Compound of 艶 (つや, 'gloss, charm, romance') and 事 (こと, 'thing, matter'). The exact historical derivation is uncertain, but the combination naturally yields the meaning 'romantic matter'.