The very first paragraph of the first story in this collection, "A Scandal in Bohemia," includes the following line: "[Holmes] was, I take it, the most perfect reasoning and observing machine that the world has seen." Part of Sherlock Holmes's attraction, both for Watson as his narrator and for the readers, is the guy's superbly disciplined mind. Conan Doyle emphasizes Holmes's magnificent brain in many ways: he uses Watson's admiration to reinforce the reader's own. He gives Holmes lots of foils, including incompetent cops and the criminals he's hunting. And perhaps the best trick of all, Holmes frequently gets to show off his smarts by wowing his clients with how much he can guess about them just by looking at their outward appearances.
As a detective working outside of official legal channels, Sherlock Holmes has more freedom than policemen like Inspector Lestrade to dispense justice directly (and as he sees fit) to the criminals he catches.
By making Watson a strong character in his own right, with both medical and literary proficiency, Conan Doyle makes Watson's admiration of Holmes's intelligence even more meaningful to the reader.