Here's the story:
* Watson finds a valuable blue carbuncle stone in the goose he buys for Christmas dinner.
* Knowing that the stone is likely stolen, he decides to return it to its rightful owner anonymously.
* To do this, he uses the alias "Henry Baker" and leaves the stone at Sherlock Holmes's lodgings.
* The story then follows Sherlock Holmes's investigation into the theft and the true identity of "Henry Baker."
So, in essence, Henry Baker is not a real person; it's simply a name used by John Watson to protect himself while trying to do the right thing.