Those are other eggs that were developing inside the main egg. I am not exactly sure of the mechanism of how that happens, but others have posted about it before. Someone posted a Youtube video a week or so ago in which a chicken egg had a whole other egg inside it.
I wouldn't worry about it, likly it was a partially formed section of egg that accidentally went back up inside and then enveloped again on it's way out.
Wow--that's bizarre. And--ew. Very weird. Egg in egg sounds plausible though--I once saw a "scientific" photo of a dead hen with her insides pulled out to show the developing eggs--it was very gross--and the less developed eggs certainly looked a lot like what you have there.
I bet she'll be fine, anyway. The development of an egg is such an intricate process that the amazing part is that so many eggs come out looking "normal."