Peter had denied Jesus three times, so Jesus got him to profess his love three times. But there's more than the number three linking these two stories. There's also the fact that both happened near a fire. When Peter denied Jesus, Peter was warming himself near a fire. When Jesus asked "Do you love me?", he was near a fire with fish cooking on it.
There's also the fact that both stories happened near dawn: The denial story, which is profoundly tragic in mood, is set in the dark of night, just before the dawn is signaled by a cock. The profession of love scene, hope-filled and positive in mood, is set just after the dawn, in the increasing light of early morning.
Jesus chose this scene-of-the-crime setting to bring about a complete healing of memories in Peter's mind. To scrub every bit of charcoal from his heart. As the penny fell about being in a fire place for a second time, Peter might well have said "touche`, (Yes) Lord, you know I love you."
At the first fire, Peter "wept bitterly." The Gospel doesn't say it, but we might well expect that at the second fire Peter also cried - tears of joy and love as well as sorrow.
To bring about deeper healing and cleansing in our own minds and hearts, we can recall our own fireplaces and dawns, as we say with Peter and maybe with tears:
"Lord, You know I love you. Lord, You know I love You. Lord, you know I love you.