The "ill" status effect is inflicted when you fight sewage eels in Golgotha.  If you see a red message in the message buffer saying that the sludge splashes into your mouth and that you gag, then that means you've become ill.

You also become ill after poison wears off, or when eating a corpse or raw meat if you are not a carnivore.

While you're ill, you don't heal naturally, even if you have the Regeneration mutation.  The condition seems to abate over time, or at least it did on my character with regeneration.