Feathers! They help keep birds warm in winter and cool in summer (i.e. thermoregulation or an animal's ability to regulate their own temperature). They protect the skin from injury. They help with flying and running (also called wing assisted locomotion). They can be different colours, depending on the breed, and can signal maturity or dominance. Their loss or absence may also indicate behaviour problems in the flock.
Chickens are naturally curious and spend large amounts of their time exploring their environment. Pecking is one of the main ways that chickens investigate the world around them. Pecking behaviour is a broad category that includes foraging behaviour as well as aggressive and feather pecking behaviour.
Feather scoring is a method of assessing the feather condition of birds to see if there are any early warning signs of issues developing in the flock. The location and degree of feather damage, if there is any, may point to a specific issue. Feather damage may be caused by the housing equipment (e.g. abrasion from the feed trough or wire floor) or different types of pecking behaviour. Aggressive pecking may result in feather loss on the head and neck. In contrast, severe feather pecking may cause feather loss at the base of the tail or belly.
Feather condition usually changes over time. As birds age, they put a lot of their energy into producing eggs and not necessarily into feather maintenance. So some degree of feather breakage and loss is normal. However, feather loss resulting in bald spots is not normal and may lead to further issues (e.g. tissue damage) if not diagnosed early and corrected. Monitoring the flock and conducting regular assessments of feather condition are important tools for anyone with chickens.
Helpful References:
Poultry Behaviour and Welfare by Michael C. Appleby, Joy A. Mench and Barry O. Hughes (CABI Publishing, 2004). Pp 83--86.
The Behavioural Biology of Chickens by Christine J. Nicol (CABI Publishing, 2015). Pp 174--176
FeatherWel -- A UK initiative that "aims to provide advice on practical strategies to reduce the risk of injurious pecking occurring in non-cage laying hens during both the rearing and laying periods." See the report here
Hennovation -- A project out of the EU, "the Hennovation project demonstrated the potential of innovation led by farmers and industry practices in two areas of concern, Injurious Pecking and End-of-Lay, during transport and at the abattoir." See the report here