I'll try for the shorty answer:
CYA, or stabilizer, slows down chlorine breakdown. This is really important in the sunlight as UV can break it down in as little as 15 minutes.

So CYA slows down and stretches that time. But there's a catch: It also slows down and inhibits the ability to neutralize contaminants. So you need a higher residual level of chlorine to maintain the same sanitation level.

That's really it in a nutshell. That's why some CYA--generally 30-50ppm is necessary and good, but more is a problem.

HOWEVER---with proper testing (Ben's kit and similar kits) you can compensate for higher CYA with higher residuals of chlorine than are normally measurable in standard kits. Since the chlorine's action has been inhibited, it's no more dangerous to swim in high CYA/High chlorine pools than other pools IF (and only if) both are properly maintained.

That's why I don't like going in any pool but mine: I KNOW how well it's maintained. Of course I'd have no problem jumping in the pools of my fellow PoolForum denizens--unless it's too dang cold (right, Poconos?)