QR barcodes are those odd-looking square codes you see around more and more; unlike standard UPC type barcodes, which only contain a short string, QR codes are meant to hold longer strings. They can hold phone numbers, e-mail addresses, or -- most often -- URLs. Most smartphones have bar-code-scanner apps that can read them, so if you scan a QR code, you can bip to an associated website easily.
For instance, here is a QR code that contains a link to the Water Cooler here:
...if you scan that with a QR reader app on an iPhone or Android phone, it will say 'URL found!' and offer to bring you right to the Absolute Write forum. These sort of codes are often used in advertising (scan the code on the bus-station poster) or other printed things; the 'Google Places' stickers a store can get contain a QR code for that store's Places entry, so you can walk past a window, scan the code, and read reviews (or review it yourself).
Presumably what PA is offering is to create a QR code for the writer's website and stick it on the cover. Since there are plenty of free QR generators out there (like the one I used to generate the AWWC link above), and it takes all of 30 seconds to generate a QR code, charging for this seems a little ridiculous. (But, well... this is PA...)