Nightingale Shadow is a power the Dragonborn can receive at the end of the Thieves Guild questline. This power allows the user to turn invisible for 120 seconds. It only activates when in sneak mode, and can deactivate when activating anything or attacking. To turn invisible again, stand up and go back into sneak mode. In addition, the power doesn't grant the effects of the Muffle spell, so the Dragonborn can still be heard by enemies while invisible. Like most other powers, this can only be used once a day.
While the three agents of Nocturnal are referred to as Agent of Shadow, Agent of Strife and Agent of Subterfuge, and the two other skills are called Nightingale Strife and Nightingale Subterfuge, this Shadow skill is actually called Shadowcloak of Nocturnal.