With time usually comes wisdom along with an enlightened perception of events and circumstances which took place.
Time "heals old wounds" because life goes on and our focus changes. Gradually you stop (dwelling) on the past.
Eventually everyone is forced to operate in the NOW in order to make the most of their life. The pain lingers when your mind lingers.
Pain is associated with a moment in time. In order to "heal" on many levels you have to let go to move on. Tomorrow is another day.
"The woods are lovely, dark and deep,
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep."
- Stopping by Woods on a Snowy Evening, Robert Frost