The Raudal de la Magdalena is the underground spring that has supplied Jaén with water since at least Roman times. The Moorish city was built around it; the great central mosque (now the Iglesia de la Magdalena) sat right next to it. A vaulted cistern carries the water through stone channels into the church's cloister, where you can still see the pool the spring once filled.
The cistern is normally closed but is opened occasionally for guided tours. Check at the tourist office. Even from outside, the surrounding small streets — quiet, almost rural — give a sense of how the medieval city lived.