Watson is our first-person narrator in all of the stories in The Return of Sherlock Holmes. He acts as a sort of hagiographic historian here. That's a fancy way of saying that his purpose is to tell us stories about how awesome his BFF Sherlock Holmes is. Hagiographic, or hagiography, is a term that refers to the biography of a saint. And saints' biographies tend to be flattering. You aren't likely to find some sort of VH1 Behind the Music-type of special of Mother Theresa after all. So Watson is a very flattering biographer for Holmes. He's also an historian. He gathers together notes, newspaper clippings, etc. and decides which cases to share with the public. There's a touch of a memoirist here as well, since Watson is recording his own memories of Holmes and their adventures for readers.
Understanding what Watson is trying to do is important, since it helps us to better understand how he's doing it. While Watson narrates these stories in the first person, he spends most of his time talking about Holmes as opposed to himself. We get detailed descriptions of everything from Holmes's facial expressions, to his dialogue, to his views on suspects. We also get some of Watson's own thoughts and observations, but we often don't have mentions of his actions or his dialogue. With a first-person narrative, we are inside the head of our narrator, in this case Watson. So we see through Watson, which means that we mainly see Holmes.
Since Watson is telling the story himself, we see what he sees and hear what he thinks, but we often don't see what Watson himself is doing in scenes. This is a bit unusual for a first-person narrative, since the narrator often tells us all about him or herself and his or her actions. But Watson is telling us a story about someone else; he hasn't made himself the main character here, so we end up getting a fuller view of Holmes (or Watson's view of Holmes) than of Watson himself.
Whenever you have a first-person narrator, you often run into issues of reliable vs. unreliable narrators. Unreliable doesn't have to mean a liar; it can also mean someone who is biased or is limited in their view. Scout in To Kill a Mockingbird is an unreliable narrator in lots of ways since she's telling us a story from a child's limited perspective; all the first person narrators in Faulkner's The Sound and the Fury are unreliable since they are all some combination of unstable, biased, uninformed, or liars.
Watson, though, is a pretty reliable narrator. This makes sense because Watson is trying to act as a biographer/historian of Sherlock Holmes. And even though he generally praises Holmes, he doesn't go totally overboard. Watson sometimes points out how annoying Holmes can be. It's the fact that Watson doesn't try to hide Holmes's less desirable qualities, combined with his self-proclaimed historian role, that makes Watson a somewhat unusually reliable first-person narrator.