These eggs are from my Buff Orpingtons. They often have what looks like dirt in them--sometimes stuck to the yolk, other times little flakes or specks floating in the white. I'm 100% sure it's not from the shell or dirt that fell in; it definitely originates in the egg. What could it be?
Those are commonly called "blood spots" or "meat spots." They can happen with any hen, but some hens do seem especially prone to them. The cause is little bits of bleeding inside the hen, or little bits of tissue that come loose inside her. They typically do not cause any problems for the hen, and are safe to eat (but even though they are safe to eat, they may not be appetizing, so many people pick them out, or cook the egg in something like brownies that disguises them, or cook the egg to feed to the chickens or a dog.)