I wonder what exactly is a man-rated rocket....

That's what the Shuttle was supposed to be. Right from the start, the solid rocket boosters were never used for manned spaceships; everybody knew it and yet, Challenger happened. The SRBs were considered simple therefore reliable technology.
Could SRB be considered man-rated? Or is it just a "theory" and a figure of style...(like saying the Shuttle is "operational") and has more to do with politics.

The Ariane 5 rocket was considered first a commercial rocket that could become man-rated (for the former Hermes lifting body), and yet, I read (here and there) that an existing rocket cannot become man-rated, but rather only newly conceived rockets could be qualified that way right from their conception.

But what about this:
Not a single (non man-rated) Ariane rocket ever exploded at the launchpad. Some have been destroyed but always at a certain altitude and speed, one even licked the launch tower with its flames and had to be destroyed several seconds (or even more than a minute) later.
From the moment a manned spaceship has a launch escape tower and the main rocket is certified as not to be destroyed at or near the launchpad, I'd consider it as man-rated.

It's of course very subjective, as well as determining it's rate of success. It's an illusion to consider that any rocket has a success rate better than 98%. So long as when a failure occures, there's a way out of danger, it should be man-rated.