First of all, Sherlock Holmes basically has his own cheering section in the form of Dr. John Watson, a man who has devoted his literary life to following Holmes around and seeing what he does. That's a lot of admiration right there. But beyond simply giving a plot-level reason for Watson to keep writing all of these stories, admiration has a formal role in making the world of Holmes work. As Holmes repeats his feats of reasoning in every story of this volume, he is constantly working to gain the trust of his clients. On a larger level, though, he's working to reassure the reader that, within the fictional world of these stories, Holmes's methods are beyond question. After all, we can only enjoy a mystery story if we believe its chain of deduction. The admiration and respect Holmes draws from his clients and his colleagues go a long way to convincing the readers that it's worth appreciating him, too.
Watson's admiration for Holmes encourages the reader to appreciate the Great Detective just as much.
The physical surprise that people like Jabez Wilson ("The Red-Headed League") and Violet Hunter ("The Copper Beeches") show when Holmes performs his usual deductions reminds the reader of just how extraordinary Holmes is meant to be.