A remanufactured cartridge is an old one that's been recycled, probably not by the original manufacturer - they clean it, reset any electronic stuff that's on it and put some new ink in it. That's not something you could do yourself, although you can get refill kits.
Especially in Canon Printer Inks The advantage of a remanufactured cartridge to the user is usually that they cost less to buy. The printer manufacturers invariably tell you that remanufactured cartridges are bad for your printer and use inferior ink but that's just them trying to persuade you to buy new ones. To my mind printers go fairly horrendously wrong from time to time regardless of the ink used.