In the wild, a bird plucking its feathers can mean many things. It could be part of the bird’s preening or grooming routine. Some species pluck their feathers to line their nests during breeding season. With captive or pet birds, it’s a different story: plucking of feathers could mean health or environmental problems.

Bring your pet bird to an avian vet to determine if it has a health problem. If the veterinarian declares your bird free of medical problem, the issue could be environmental. Birds tend to pluck their feathers when they are bored or are under stress. Find out the cause of the problem - Is it the food? Is your bird getting enough interaction or mental stimulation? Is the cage clean and spacious enough for them? Once you have discovered what makes your bird feel uncomfortable, work on it immediately. Providing your bird with a preening toy may also help keep your pet bird from plucking its own feathers. 

Remember, though, that birds, unlike cats and dogs, are never completely domesticable living species. You can put them in a cage, but you can never completely cage them. As such, they retain many of their habits that are natural to them in the wild - one of these is preening and plucking feathers. So if your pet is plucking feathers purely instinctually, it is probably not a good idea to make them stop.