Panniers are the bags on your bike that store all your stuff. They typically mount over your wheels, either in the front or the back, or both. They are most commonly used for long-distance touring or to haul stuff around town.
Panniers are usually mounted on racks that are bolted onto the bike frame. These frames both bear the weight of the load and keep the bags from getting into the spokes. Panniers can be water-tight or can be outfitted with external covers that fit over them like a shower cap in the event of precipitation.
Because panniers need to be very well constructed and are expected to last a long time under the demands of bike touring or utility riding, they are generally more expensive than the typical bike accessory. They are sold in pairs, and a well-made set of panniers will cost $200-300 US or more.