Fletching is usually made of plastic or feathers, and helps stabilize the bolt in flight.
The feather fletching is known to be more forgivable when shooting. This is due to the collapsible nature of the feather material. However, this same property is a downfall as they will collapse when they get wet if you are hunting in poor weather conditions.
The plastic style fletching is weather proof and good for all seasons. They do not collapse as easily, but may tear from time to time.
Whichever style of fletching you choose you need to check them often and replace them when worn.