When Watson remarks to Sherlock Holmes, "I believe you have eyes on the back of your head," what does he mean by this, and what does it say of Sherlock Holmes himself?
Having "eyes in the back of your head" is an old idiom often used by students whose teacher seemed able to perceive everything that they did, even if she/he were not facing the students. It was also used to characterize one's mother, too, who also seemed omniscient about her children's behaviors.
In Chapter One of The Hound of the Baskervilles, Mr. Watson visits his old friend Sherlock Holmes, who, surprisingly sits at the breakfast table (Holmes is usually up late each night). As Holmes sits with his back to Mr. Watson, Watson picks up the walking stick of Mr. James Mortimer and reads the inscription upon it. At this point, without turning around or giving any suggestion of paying attention to Watson, Holmes asks Watson, "Well, Watson, what do you make of it?" Watson reacts,
"How did you know what I was doing? I believe you have eyes in the back of your head."
Holmes responds that he has watched Watson in his "well-polished, silver-plated coffee-pot" that is in front of him, demonstrating once again the keen powers of perception for which Sherlock Holmes is renowned.
The phrase "having eyes in the back of your head" is interpred as having the ability to know what is going on literally behind your back. This is illustrated perfectly in this scene. These two men see things in a contrasting way: Watson is somewhat impressed that Sherlock knew he was examining the walking stick while Sherlock, in his usual pragmatic way, is highly preceptive and explains that he could see Watson's reflection on the pot therefore proving his belief that everything is a matter of perspective.