Reilly is a GMAC employee who keeps phoning Jerry Lundegaard and asking him for serial numbers pertaining to cars that are supposedly being sold at the dealership. (GMAC was a finance company that provided auto loans.) At one point he says, "Yeah, but we have an audit here, I just have to know that these vehicles you're financing with this money, that they really exist." To which Jerry replies, unconvincingly, "Yah, well, they exist all right."
Jerry doesn't seem very confident when he says this, so it's likely that Jerry is scamming GMAC. Perhaps he's using the money for whatever debt he secretly owes, and is pretending to be financing the purchase of cars for the dealership to sell, when, in reality there are no cars.
At any rate, Reilly's polite but extremely persistent and firm in his demands. By the end of the movie, he says that if he doesn't get the serial numbers soon, he'll be forced to consult the legal department. By then, Jerry's already well on his way to being arrested for the kidnapping plot.