Yext is a company that helps all sorts of businesses to update multiple local directory listings from one place. Yext does charge for this service, which can be quite pricey depending on which level of service you choose.
MapQuest has now announced that they are sutting down their Local Business Center listings (free, basic MapQuest listing) and have partnered with Yext to allow listings to be edited. This means that if you want to edit your MapQuest listing, you will be required to pay Yext to do so. As of now, the fee is set at $3.00 per week for MapQuest only, which translates to $156 per year.
I don't see any way around this, so if your MapQuest listing information is incorrect, you may be forced to use Yext in order to correct your listing. If your MapQuest listing is correct, you shouldn't need to do anything.
Edited 01/29/2014: A big thank you to Steve Hiatt of Bottger Mansion of Old Town, who found a way to update your own listing one per year via LocalEze, thus bypassing Yext. Find that information HERE.
Local, Social Media and Education Manager