A character sketch is a complete description of a person.  It usually does include both physical and personality traits.

James Watson is a doctor, and he is highly observant and curious.  Unfortunately, he is no match for his mentor and friend Sherlock Holmes, the great detective.  Watson struggles to be the kind of detective that Holmes is.  For example, when Watson tries to deduce information about the carrier of a walking stick.

“I am afraid, my dear Watson, that most of your conclusions were erroneous. When I said that you stimulated me I meant, to be frank, that in noting your fallacies I was occasionally guided towards the truth. Not that you are entirely wrong in this instance.” (enotes full text pdf p. 5)

Watson is disappointed and somewhat frustrated that he is wrong.  Holmes seems to expect it, and in fact appears impressed that Watson achieved what little observation he did.  Holmes does not think highly of Watson’s abilities in this area, and this frustrates Watson.

Watson is eager and loyal.  He is hurt when Holmes does not tell him his plans, but he always follows orders precisely. 

There is actually very little to describe Watson other than in bits and pieces throughout the stories.  He seems to have been injured in the Afghanistan war, and may limp somewhat, but in The Hound of Baskervilles he is able to jaunt across the moor with little difficulty.  He is much more uptight than Holmes, and Holmes often notes exactly how much weight he has gained so he might be somewhat slim.

Watson carries a gun, and seems to physically know how to handle himself (though he is not likely as strong or agile as the once-boxer Holmes).  He also smokes tobacco.