If you win a battle against a noble, you have a chance that the lord or king can be taken prisoner, along with the troops (if any) who were knocked unconscious. You can also let the nobles go, netting you honor and probably a relationship bonus (some lords don't like being released). If you chose to keep them, you lose relationship, but later have a chance to ransom the captured noble back to the opposing faction, giving you 1,000-6,000 denars for a vassal and 9,000-18,000 denars for a king.