The blue carbuncle is a very valuable jewel that belongs to the Countess of Morcar. It is worth a huge amount of money.
It is stolen by a man named James Ryder. He is the "Head Attendant" at the hotel where the Countess was staying and where the jewel was stolen.
He admits to Holmes all that he did and explains it to him in detail. Holmes decides to let him go. Ryder says he will leave the country and that will let Horner off the hook. Holmes decides that Ryder will never commit another crime and, besides, it's Christmas time and he feels forgiving.