The physical problem of atrophy with clipping is twofold. One is the atrophy of the muscles that move the wings and how these are affected as has been very graphically described by Greycloud. But this does not only affect the wings themselves, it also affects their breathing and their laying because the muscles that move the wings continue down their chest and onto their abdomen - and these are the same muscles that females use for laying eggs (canary breeders did not know why but they did know that hens that flew laid better than hens that did not and that's why they have been keeping the hens in flight cages during the resting season for hundreds of years even when they kept the males in tiny cages). As to their breathing, birds do not have a diaphragm, like we do, their lungs are almost rigid and the air flows through them by the bellowing effect of the air sacs which are, in turn, moved by the same muscles that move the wings so, when they don't fly and those muscles atrophy, they end up with diminished lung capacity, a dangerous thing (it killed my mother) and one of the reasons why pet birds suffer from respiratory infections so very often. The most important link between flying and breathing comes from the fact that the posterior air sacs can only be fully utilized during flight. This was observed in studies of birds flying in wind tunnels equiped with XRay machines. No flight, no full extension of posterior air sacs which means partial atrophy. And having any internal organ atrophy, even if it's only partially, is never a good thing because it makes it more prone to infection (cannot cleanse itself out naturally) but most especially the air sacs because the avian respiratory system is one-way and not two-ways like ours (the air sacs are connected between themselves and with the lungs with the air flowing from one to the other in sequence -and that's also why birds cannot cough, because the air that goes in is not the same air that comes out next, it needs to go through all the different air sacs) so when there is infection in one air sac, chances are, it will end up in all the others because the bacteria, virus, fungus or parasite will 'travel' with the air from one to the other.