Once, Holmes tells Watson that he dislikes the way Watson narrates the stories. He feels that they are too romantic. "Crime is common, logic is rare," says Holmes in "The Adventure of the Copper Beeches." Holmes wants Watson to focus on the logic, the cold, hard, systematic reasoning that is used to discover the truth behind crime. He feels that Watson embellishes the facts and makes them into stories. Watson is naturally upset and asks Holmes why he does not write them himself. Holmes says that he will, but when he retires.
So this was the explanation given by the fictional character in the stories.
As for why Doyle decided to have Watson narrate much of the stories, it might have been due to the influence of Edgar Allen Poe's Detective Dupin. Poe's Dupin has many similarities to Sherlock Holmes. In fact, this is mentioned in "A Study In Scarlet." Edgar Allen Poe is often credited with having established the first detective character in fiction. Many authors followed in his footsteps. Dupin's stories were also narrated by a friend and roommate who accompanied Dupin on his investigations. It's very possible that Doyle simply wanted to continue with the same format.
Sherlock Holmes, while much more attracted to the spotlight than he might let on, is not one for narrative flourishes. Violent emotions and sentiment are not his strong points. He is all about the cold facts, picking up details and following them to their logical conclusion. While this make him a great detective, it makes him a poor story-teller. One just has to take a look through "The Adventure of the Lion's Mane," narrated by Holmes rather than Watson, to see how unconcerned Holmes is with injecting any enhancing flourishes that would turn it from a case to a story. For example, there is a huge chunk of dialogue because Holmes is simply recording the event verbatim, offering no inner reflections or observations, no thought process behind why he chooses his questions. To be fair, giving voice to too many of his thoughts would likely result in the mystery being solved for the reader, but that's just the point- Watson's narration allows the mystery to long remain a mystery while still having the opportunity to add his own nervous, awed, or other emotional impressions of the events to make it read like more than just a straight case file. Watson is in a sense the heart to Holmes' brain, giving Watson all the "silly" human feelings that help to color the stories. Even Holmes, who often chides Watson for the way he records their cases, cannot help but acknowledge the unfortunate lack of Watson's narrative flair.
"Ah! had he but been with me, how much he might have made of so wonderful a happening and of my eventual triumph against every difficulty! As it is, however, I must needs tell my tale in my own plain way..."
this is a very good answer and i would only add one thing to it. Simply that there would be no element of surprise if all the stories were written by holmes himself. by narrating it, it would seem less of a mystery. if you see it through holmes's point of view then either the charecter must conceal something from the reader, which is mildly annoying whilst reading it, or the narrator must share all his thoughts in which case there would be no mystery. Most detective novels are written from a third point of view such as the agatha christies.
Arthur Conan Doyle's The Hound of the Baskerville is told from Dr. Watwon's point of view. This is true for the short stories as well, though one of the Holmes stories is told in the third person; two are narrated by Holmes himself; and all the rest are narrated by John H. Watson, M.D.
The reason that Watson narrates the stories is that Watwon is a thoroughly reliable narrator: the embodiment of common sense, decency, and domesticity. He serves as a counterbalance to the other characters and to Holmes himself. He also serves as a surrogate for the reader. The two stories narrated by Holmes are not very good, since Watson’s absence is felt and Holmes often seems to be concealing something.
To examine narration a little further, Watson’s predictability, his flatness, is part of what makes him so endearing and is perhaps crucial to his effectiveness as the narrator. Holmes has a number of eccentricities and a dark side; this dark side may interfere and cloud the many small details that are uncovered in the stories, and principally, he never really surprises us.