One's inner thoughts or true intention; the inmost heart.
彼の内心はなかなか読めない。
You can't easily read his inner thoughts.
表面的には笑っていたが、内心は不安でいっぱいだった。
Although she smiled on the surface, she was filled with anxiety deep down.
内心を打ち明けるのは信頼が必要だ。
Confessing one's inner thoughts requires trust.
Adverbial: 'at heart' or 'deep down' — indicating what one actually feels on the inside.
彼は優しいと言っていたが、内心では勝てると思っていた。
He said he was kind, but deep down he thought he could win.
内心、辞めたいと思っているが言えないでいる。
Deep down, I want to quit, but I can't say it.
In mathematics: the incenter of a figure (e.g., the center of an inscribed circle in a triangle).
三角形の内心は三つの角の二等分線の交点である。
The incenter of a triangle is the intersection point of the three angle bisectors.