This is a brief description of what happens to an egg duing the final few days of incubation as it comes up to hatching.........
The nearly fully grown embryo begins to produce more carbon dioxide (from the waste processes of its development) than can be easily disposed of and as it begins to build up within the egg the hatching process begins.
The muscularis complexus (the pipping muscle) at the back of the neck begins twitching. First the chick's head comes up and out from under its wing , and the sharp egg tooth on the end of its beak will puncture the inner shell membrane and its beak will enter the air cell. If you are hatching white or pale shelled eggs this is apparent on candling, but on the darker shelled eggs, this process is often impossible to see, even when candling in a totally darkened room.
With its beak in the air sac the chick is able to take its first breaths of air, and the lungs begin to function. The piecing of this inner membrane will cause changes in the blood vessels which have covered the embryo and acted as a "placenta", and they will begin to shut down. All the blood from these vessels must drain into the embryo/chick before it is ready to hatch - a small chick has very little blood and needs it all.
As the supply of oxygen in the air sac is gradually used it is replaced with cabon dioxide exhaled by the chick. This imbalance again begins to suffocate the nearly hatched chick, and as it does so it will begin to twitch in its death/birth throws once more, and it is this violent twitching which causes the chick to "pip" through the egg shell. Eggs are shaped so that although extremely strong under pressure from the outside, they are very easy to break from the inside.
The egg shell is now "pipped" and the chick can once more breath fresh air.
Normally after this trauma the chick will take some time to rest, which will allow the final network of blood vessels to drain down into the chick. Abdominal muscles begin twitching, which helps draw the yolk sac into the coelom. Leg muscle twitching helps strengthen the legs, and the chick should now begin to struggle to escape the shell, and with each effort to escape, it will, as a result of the angle the embryo has been contained within the shell, rotate slightly, so each time the egg tooth comes in contact with a fresh section of shell, and this is what causes the circular pipping of the egg.
Furthermore with each muscular contraction more of the egg yolk is drawn inside the chicks abdomen. This egg yolk will feed the chick for the first 72 hours after pipping, allowing the chick to survive without food or water, and in fact if newly hatched chicks are fed to early this can hinder the full utilization of the egg yolk, and lead to unthrifty chicks, in a similar way that young mammals deprived of colostrum are more suseptible to sucumb to disease.
You can see from the above description, that to intervene in the hatching process is to run risks. I have no doubt that some chicks will survive after intervention, when they might otherwise have perished before escaping the shell, and if such a bird is a show bird, bred for its particular feather colour, or some specific feature of its conformity, and on which care (and perhaps veterinary treatment) may need to be lavished over its lifetime, then this may not too much of a problem. If, however, a breeder is intent on producing strong healthy and productive stock, then to "help" out a weakly hatching chick may lead to a flock of "poor-doers".
Personally I feel it is best for nature to take its course, but if you do decide to "help" an egg to hatch then always start from the air sac, work in small sections and allow the chick time to revive between. If it starts to bleed at all stop immediately, and replace in the hatcher for an hour or so. If you can leave at least some of the shell on so the chick must at least make a little effort it will help draw the egg sac inside - it is vital this has happened, as a chick which has not absorbed its yolk properly will probably die within the the first fortnight in any case, and if it develops an infection in its unhealed navel it could infect any other hatchlings and more deaths may occur.