Mr. Riley is an auctioneer and a friend of the Tulliver family. Though he only appears in a few chapters very early in the book (we find out he dies in the middle of the novel), he plays a very important role. Mr. Riley is the person who suggests that Mr. Tulliver send Tom to school with Mr. Stelling. This of course sets off a whole chain of events that results in the Tulliver kids forming a close connection with Philip Wakem.
Mr. Riley also helps to demonstrate one of the book’s major themes: that of the "artificial" or fake nature of people in society. Mr. Riley basically pretends to know more about Mr. Stelling than he does, because he doesn’t want to appear ill-informed and because he hopes to form a beneficial connection with Mr. Stelling and his family. Mr. Riley’s exaggeration has long-ranging consequences, though.