A cloaking shadow functioned as a tracking device. It was affixed to a starship's transponder, which then enabled other ships to tail it.
It was generally employed for covert tracking, exemplified by Obi-Wan Kenobi's placement of such a beacon on Slave I. This allowed him to follow the ship's journey from Kamino to Geonosis. The tracking signal's close integration with the ship's transponder signal often made it difficult for the targeted ship's crew to detect the "shadow" transmission.
The Yuuzhan Vong also utilized a device referred to by this name on their Yorik-stronha spyships. This might relate to their function as clandestine vanguard ships, directing invasion fleets.
The New Essential Guide to Weapons and Technology mentions the use of a "cloaking shadow" on the Yorik-stronha. While it's presumed to be a beacon, within this context, the phrase could alternatively denote a type of Yuuzhan Vong cloaking device.