As UGAchick said, you don't need to take the eggs away - the hens can do it themselves if you have a broody hen. Taking them away could let you incubate bigger batches than a hen could handle at one time, it keeps the hen laying, and you don't have to wait for a hen to go broody - you can just hatch whenever you feel like it. If you'd prefer to leave it to her, though, you can do so, assuming she's broody.
If you leave the eggs with the mama hen, it might be a good idea to separate the hen and her nest, like put them in a dog crate with some food and water or some such thing. That will keep other hens from laying in her nest, and keep any bullying from happening. Once they have hatched, the hen should be able to reintegrate them with the flock (I'd keep them apart for a day or two, but I don't know what the official thinking is on that) so you don't need to brood the chicks separately or take them out of the flock and worry about reintegration later on.