The appearance of Jim's watch foreshadows the watch being sold later in the story.
Now, there were two possessions of the James Dillingham Youngs in which they both took a mighty pride. One was Jim's gold watch that had been his father's and grandfather's. [...] Had King Solomon been the janitor, with all his treasures piled up in the basement, Jim would have pulled out his watch every time he passed, just to see him pluck at his beard from envy.
Della has just been looking at her luxuriant hair in the mirror, making up her mind to sell it so that she can afford to buy Jim a gift. Jim's watch is described in the same paragraph, equating its value to that of Della's hair. At this point, that's where the comparison ends. Since the story mostly follows Della's perspective, there's no other apparent reason why Jim's watch gets mentioned at this point, except to underline the Youngs' poverty (they have so few valuable possessions) and the fact that they assign great sentimental value to what few things they have.
Later, Della ends up selling her hair in order to buy Jim an ornamental chain to display the watch. But by equating the watch's value to the value of Della's hair at this point, the story hints that the watch will come to have additional significance, too. Because Della sells her hair, the reader is prompted to expect that Jim will also sell his watch—setting up the story's big twist.