To take something to heart; to strongly imprint a lesson or admonition on one's mind so as not to forget it.
上司からの注意を肝に銘じて、次は同じ失敗を繰り返さないようにする。
I'll take my boss's warning to heart and make sure not to repeat the same mistake.
この言葉を肝に銘じて、日々の行動に生かします。
I'll keep this saying in mind and apply it to my daily actions.
あの失敗は肝に銘じるべき教訓だ。
That failure is a lesson to be deeply remembered.