TL;DR: We are never told anything exact, but the protagonist seems to believe that John Coffey has been wandering around the South for years, surviving on odd jobs & healing people.
WHAT is John Coffey: Nature & Ability
Like many of Stephen King's works, we are never given a definitive answer as to WHAT John Coffey is or how his abilities work exactly. The book never states that he is an angel, though he IS referred to as "a gift from God". It would seem that what he removes from a person - the black smoke and insects - is the "evil" from their body. In some cases, this is simply illness, but in other cases it's more. The warden's wife, for example, seems to have been
possessed by multiple demons, all of which John inhaled and later put into Percy.
In addition to his healing ability, Coffey could also know a person's true nature simply by touching them. This ability is demonstrated with both Percy AND Wharton (an inmate). Coffey also alludes to it when he tells the protagonist that he knows what a good man he is although they just met.
WHO is John Coffey: Scars & Past History
As for his previous history and scars, there is speculation among the guards that he was heavily abused when he was a child. Several references are made to how the scars resemble whip-marks and criss-cross his skin all over. The conversation you cite in the film doesn't exist, but a similar one occurs between two guards:
"Have you seen the scars on him?" Hammersmith asked abruptly. He was
still watching his kids, who couldn't quite bring themselves to
abandon the pleasures of the swing - not even for oatmeal-raisin
"Yes." But I was surprised he had.
He saw my reaction and laughed. "The defense attorney's one big
victory was getting Coffey to take off his shirt and show those scars
to the jury. The prosecutor, George Peterson, objected like hell, but
the judge allowed it. Old George could have saved, his breath - juries
around these parts don't buy all that psychology crap about how people
who've been mistreated just can't help themselves. They believe people
can help themselves. It's a point of view I have a lot of sympathy for
- but those scars were pretty ghastly, just the same. Notice anything about them, Edgecombe?"
I had seen the man naked in the shower, and I'd noticed, all right; I
knew just what he was talking about.
"They're all broken up. Latticed, almost."
"You know what that means?"
"Somebody whopped the living hell out of him when he was a kid," I
said. "Before he grew."
This would seem to indicate that he was beaten & abused as a child. Seeing as how the protagonist
lived to be over 104 years old after being healed by Coffey, yet only appeared 80,
it's entirely possible that Coffey is far older than he looks. And Coffey himself states that some of the scars are so old, even he can't remember where they came from. If we were to speculate, we could even hypothesize that Coffey was a former slave, which would make him about 80 years old in 1934. Regardless, the protagonist was able to track down rumors all over the South (and going back several years) of a large black man doing odd jobs in towns, only to disappear later after some tragedy or when someone was miraculously healed of illness.