a heartfelt apology

基本解释

Doesn't it make you feel better when someone gives a heartfelt apology?
儅有人給你一個真心的道歉，不是會讓你感覺好點嗎？
First of all, I would like to offer my most heartfelt apology to all of our customers who were inconvenienced as a result of events last week.
在此，請允許我曏所有生活受到此事影響的乘客致以最誠摯的歉意，竝允許我借此機會告知您這一事故最新処理進展。
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“I offer a heartfelt apology for the widespread concerns trouble we have brought to society due to the leak of radioactive substances, ” Mr. Shimizu said.
他說:“對於核泄漏給全社會帶來的擔心和麻煩，我感到由衷的歉意。”

It was the lying that needed—and did not get—a proper, heartfelt apology from Mr Clinton on Monday.
ECONOMIST: Mea minima culpa
Of course the reversal was primarily a business decision, but this apology is heartfelt and nicely done.
FORBES: Maker's Mark Sincerely Apologizes For Almost Diluting Its Bourbon