Gooseberry is a young boy, probably an orphan, whose real name is Octavius Guy. He is one of the street children that populated literature at the time. While he only shows up for a few pages, he is integral to the plot, as he follows the mysterious sailor who has received a package from Luker, who is suspected of hiding the Moonstone at a bank. Gooseberry follows him and discovers that he was trying to board a boat.
...a small boy, dressed in a jacket and trousers of threadbare black cloth, and personally remarkable in virtue of the extraordinary prominence of his eyes. They projected so far, and they rolled about so loosely, that you wondered uneasily why they remained in their sockets.
(Collins, The Moonstone, gutenberg.org)
Gooseberry is not present for the denouement, but his information is essential to clearing up the story, and the identity of the true thief. Had he not followed the "sailor," revealed to be Godfrey Ablewhite, the stone would still have been retrieved by its original owners, but the protagonists of the story would have been hard-pressed to discover what had happened. In this way, Gooseberry is a minor character who serves an important role; although he does not undergo any significant characterization or arc, he ends up being important.