For breeding chickens, not just general care. That helps a lot.
You need about one rooster for every 10 hens to be pretty sure of fertility. A young active rooster can often keep more hens than this fertile, but commercial operations use one rooster for every 10 hens.
The chickens need to be fed a good diet. They don't really need more protein than a regular laying flock, but they sometimes need certain vitamins and minerals. If yours are allowed to free range, they are probably getting enough from the various things they find to eat, but if yours are contained, you might want to investigate this a little. For most of us, this really does not matter that much, but if you are going into breeding on a fairly large scale, this might be worth your time to look into. And make sure they always have plenty of water.
They need to be healthy. If they are sick, they obviously are not going to be able to lay strong healthy eggs. Check them for mites and lice. Mites and lice will suck the blood out of them, leaving them weak. Also, since they usually gather around the vent where the moisture is, they can interfere with breeding if there are too many of them. Checking for worms is also a good idea. Again, worms can drain them of energy.
You need to look at the thickness of your egg shells. You do not want them to be so thin that they break or crack easily, but you do not want them super thick either. Sometimes chicks have trouble hatching from really thick egg shells. This is usually not a big problem, but you want regular eggs, nothing extreme either way.
You want the eggs to be regular sized for that breed. Eggs that are too small or too large can have problems. What you want are decent sized regular sized eggs for that specific breed of chicken.
Hope this helps some. Good luck!