To take a peep at or catch a glimpse of something (often briefly or partially), such as an expression, situation, or aspect.
会議の途中で彼の本心を垣間見た気がした。
During the meeting I felt I caught a glimpse of his true feelings.
古い日記を読んで当時の暮らしを垣間見ることができた。
By reading the old diary I was able to glimpse what life was like at that time.
窓のすき間から庭の様子を垣間見る。
I peeped at the garden through a gap in the window.
ふと人の本性を垣間見る瞬間がある。
There are moments when you unexpectedly catch a glimpse of someone's true nature.