The Ghost is spirit who starts haunting Link after the completion of the Angler's Tunnel which wants Link to take it to its house. As he cannot enter any dungeons while the Ghost follows him, Link must help it in order to enter the Catfish's Maw. Once Link brings it to the House by the Bay north of Toronbo Shores, the Ghost examines it before saying it is essentially unchanged from what it was when it was alive.
The Ghost then asks Link to bring it to its grave, which is located in the Koholint Prairie near the Cemetary. Once there, the Ghost thanks Link and tells him to look inside one of the jars in his house to find a Secret Seashell. The seashell does not appear until after Link has fulfilled the Ghost's requests.
In the Link's Awakening manga, the Ghost is named Nakura, who is a former soldier. It saves Link's life by possessing him during his fight against Karuna and gives him a more powerful Sword after he takes it to its house.
If Link sprinkles Magic Powder on the Ghost's grave, it tells him to stop or suffer the effects of a curse. Despite this, he will not put a curse of any kind on Link.
The Poes from Oracle of Seasons resembles the Ghost, and even share the same sound effect when appearing.
The Ghost in his house
Photo of Link and the Ghost in its grave
Nakura from the Link's Awakening manga
↑"Take the Ghost where it wants to go, then trade Mr. Write's Broom for Grandma Ulrira's Fish Hook." (The Legend of Zelda: Link's Awakening Nintendo Player's Guide (Nintendo Power), pg. 57)