To do something secretly while someone else is not looking; to do something behind someone's back (often used as 〜の目を盗んで).
子どもたちは親の目を盗んで夜遅くまで起きていた。
The children stayed up late without their parents knowing.
彼は上司の目を盗んでスマホを見ていた。
He was looking at his smartphone behind his boss's back.
試験中に他人の答案を目を盗んで見るのは不正行為だ。
Looking at someone else's answers during an exam is cheating.
彼女は両親の目を盗んで友達と旅行に行った。
She went on a trip with friends without her parents knowing.