A secret; a private matter kept from others. Information shared only with close people or kept confidential (often shortened to '内緒').
それは内緒事だから、他の人には言わないでね。
That's a secret, so don't tell anyone else, okay?
子どもたちは先生に内緒事をするために相談室に行った。
The children went to the counselor's room to discuss something privately with the teacher.
二人だけの内緒事が、やがて大きな問題になった。
A secret between the two eventually became a big problem.
内緒事を守るのは信頼関係の重要な部分だ。
Keeping someone's confidences is an important part of trust.