A bag, basket, box, or container, usually used in pairs hung over the rear wheel of a bicycle.
While the dictionary explanation is fairly clear, it doesn’t begin to cover what panniers really are. Get a decent pair, and you no longer have to pack all your gear into a backpack, and arrive at your location sweaty and sore. And unlike backpacks, they are usually much better at keeping stuff dry in the rain. They can also hold more. That weight is centered over your rear wheel, not high up on your back. Organization is a lot easier too. Panniers with straps can be taken off and carried into a store, for shopping. Or take your office clothes, lunch, laptop, tablet, and everything else with you.
Panniers are not new, and have been around for years in various forms, long before the invention of the bicycle. They have been used on horses for at least two centuries. It was only 130 years ago that the first patent for bicycle panniers was issued. In 1971, the modern bicycle pannier was invented in Boulder, Colorado. Probably for carrying beer, too. Today, you can get all sorts of panniers, in a variety of sizes from small to huge. Grocery shopping? European tour? You’re covered. Detachable, waterproof, reflectorized, color-coordinated. You name it, someone makes it.
If you are just getting into commuting, going car-light or car-free, or planning an epic bike tour, you need to choose some panniers. Spend some time on the internet, and also at your local shop, and determine which features you need, then start shopping. A good set of panniers (or even a large single), may set you back a pretty penny, but taking that weight off your shoulders will be worth it.