If you read the last page of this story, the answer seems straightforward. The king says he is "immensely indebted" to Holmes for solving his problem and asks how he may reward the detective. He offers Holmes an emerald ring, but Holmes demurs, saying "Your Majesty has something which I...
If you read the last page of this story, the answer seems straightforward. The king says he is "immensely indebted" to Holmes for solving his problem and asks how he may reward the detective. He offers Holmes an emerald ring, but Holmes demurs, saying "Your Majesty has something which I should value even more highly."
Holmes says he wants the photograph he obtained from Irene Adler -- the same photograph that the king had hired Holmes to retrieve. The king seems amazed that Holmes requests so little and is happy to comply.
The event reveals something about Holmes' character. Holmes, who usually takes no personal interest in women, wants a memento of Irene Adler. She outsmarted him, and he holds her in high esteem. He indicates, sarcastically, that she is on a "very different level" than the king. Asking to keep her photo seems to be a rare instance of sentimentality on his part. It also seems like a very extravagant gesture, because he might have asked for something of great monetary value.
But we need to consider a couple of points. First, the king has already paid Holmes a great sum. At their first meeting, Holmes and the king discuss the case, and Holmes asks about money. The king replies that Holmes has "carte blanche," indicating he is willing to pay any price for the detective's services. To cover "present expenses," he gives Holmes a bag of cash -- a combination of gold coin and paper notes that totals £1,000.00.
That was a lot of money in 1891, when this story was first published. According to a historical currency converter created by Eric Nye (Department of English, University of Wyoming), it is roughly the equivalent of $128,000 today (October 3, 2016).
Second, Holmes performed relatively little work on the case, and he didn't actually obtain the photo as the result of his own efforts. Adler escaped with her photo before Holmes could retrieve it. The only reason he could present the photo to the king and reassure him that Adler posed no threat was because Alder voluntarily handed it over. The king was off the hook because Adler, for her own reasons, decided to let him off the hook. Holmes' actions weren't directly relevant. So Holmes was amply rewarded in monetary terms even before the king offered this additional reward.
Information from Eric W. Nye, Pounds Sterling to Dollars: Historical Conversion of Currency, accessed Monday, October 03, 2016.