Christopher Walken (er, the character he plays) may not play a major role in Pulp Fiction, but he has the honor of delivering a very important (and hopefully recently sanitized) item to the young Butch: his great-grandfather's gold watch.
The watch itself has obvious sentimental significance for Butch because it's been passed down through generations of his family. So the literal meaning of the watch is as a plot device, forcing Butch to return to his apartment where thing start to go downhill fast.
But the gold watch also seems to represent meaning in Butch's life—a life that otherwise doesn't have much meaning apart from survival and making money. As Butch tells Esmarelda, "I'm an American. Our names don't mean s***." The watch is a link to the men in his family whose life did have meaning. They were soldiers, men of honor who fought for their country and endured POW camps. Going back to retrieve the watch leads to the storyline in which Butch retrieves meaning and honor in his life by saving Marsellus.