Sir Arthur Conan Doyle frequently has Sherlock Holmes make deductions about his clients in the opening scenes of his stories. Typically, the visitor is astonished by what seems like psychic powers, and then Holmes explains what he observed and what he deduced from those observations. Here is an example from "The Red-Headed League."
“Beyond the obvious facts that he has at some time done manual labour, that he takes snuff, that he is a Freemason, that he has been in China, and that he has done a considerable amount of writing lately, I can deduce nothing else.”
“How, in the name of good-fortune, did you know all that, Mr. Holmes?” he asked.
Holmes then goes on to explain each of his deductions with the exception of the snuff-taking, which the reader will assume is obvious from the quantity of snuff on Jabez Wilson's waistcoat.
Doyle's main reason for having Holmes make these apparently gratuitous observations in so many of his stories is partly to demonstrate his detective's keen deductive powers. They show that Holmes is always on the alert, always observing, always making deductions from force of habit. Sometimes Holmes' deductions will convey useful information to the reader. For instance, the fact that Wilson has spent some time in China helps to explain why an unusual event like the foundation of the Red-Headed League might have occurred without his having heard about it. Wilson explains that he was a ship's carpenter, which means he was out of the country for years. When his new assistant told him all about the wealthy American who founded the Red-Headed League, Wilson would naturally assume that he had never heard about it because he was far away from England when it happened.
Like Jabez Wilson in "The Red-Headed League," Helen Stoner in "The Adventure of the Speckled Band" is astonished when Holmes describes the methods of transportation she used to get to 221B Baker Street. And, characteristically, Holmes explains his observations and deductions. This characterizes Holmes as keenly observant and highly intelligent. He doesn't miss a thing. It also serves to help the reader form a mental picture of the setting in which the story takes place. It extends from Baker Street to Stoke Moran on the western border of Surrey, from the crowded city to the sparsely populated countryside. The reader has to be given some idea of how a timid and sheltered Victorian maiden could travel to London so easily and so quickly. She can take a dog cart from the nearby Crown Inn to Leatherhead Station and get off at Waterloo Station, where she would take a cab to Baker Street. Doyle makes this exposition interesting through the dialogue, deductions, and explanations.
So Sir Arthur Conan Doyle's purpose in having Sherlock Holmes describe the methods of transportation that Helen Stoner used to reach his residence in "The Adventure of the Speckled Band" is to characterize the great detective and to convey some pertinent information to the reader in dramatic dialogue rather than in straight prose exposition. The interchange also helps the reader to visualize Helen Stoner and to become better acquainted with this extremely important character whose plight is central to the entire story.