As the clip only trims feathers and not the wings themselves, it does not cause the bird major physical harm.
Since the feathers do not have nerve endings, the bird does not feel pain. Therefore, wing clipping is in a way similar to a person having their nails clipped or their hair cut.
An appropriate wing clip will allow a bird to glide across the room without gaining altitude. If too few primaries are taken, the bird will be able to gain altitude; if too many primaries are taken, the bird will plummet like a rock. Those experienced with wing clipping will only take one or two feathers from each side at a time and see how well the bird can fly before taking more feathers, to avoid causing the bird to plummet and potentially be injured in doing so.
Many people who keep birds as pets prefer to clip their wings so that their birds will not crash into mirrors, walls, or windows, all of which are serious hazards to flighted birds: A hard crash can result in instant death.
Other people clip their birds' wings to minimize the chances of them flying away if they accidentally get outdoors. However, in the right conditions -- particularly windy days -- birds whose wings are clipped can still gain altitude and fly out of their owner's reach.
Another reason for clipping wings is to keep pet birds that are social in nature (such as parrots) more tame. When birds are unclipped, they typically have a greater sense of independence and can be less likely to socialize with their owners.
When a bird's wings are clipped, an equal number of feathers are taken from each wing. To keep a bird from being fully-flighted, wing clipping must be done after every moult. Many people clip their birds' wings themselves, although it is a good idea to have an avian veterinarian, pet store employee, or breeder demonstrate the process first.