noun
Formal or literary term for a confidential or personal matter not meant to be disclosed.
彼は密か事を打ち明けるように、声をひそめた。
He lowered his voice as if confiding a secret.
noun
secret love affair; liaison
Specifically refers to a clandestine romantic relationship; carries a literary or old-fashioned tone.
二人の密か事は、やがて周囲に知れ渡った。
Their secret love affair eventually became known to everyone around them.
秘密 is the common, everyday word for 'secret'; 密か事 is a formal/literary synonym with a more classical feel.
内緒 is casual and often used among friends or family; 密か事 is formal and rarely used in conversation.
Compound of 密か (misoka, 'secret') + 事 (koto, 'matter'). The exact historical derivation is uncertain, but the word has been used in classical and literary Japanese.