What's the black thing at the bottom of navel oranges?
I'm not as familiar with citrus, but tomatoes and peppers can develop something called blossom-end rot. This is caused by the plant not receiving enough nutrients (specifically calcium), whether b/c the plant isn't getting enough water and thus can't get the nutrients out of the soil or b/c the soil is deficient. 

Regarding whether it's safe to eat, a tomato w/ blossom end rot is still safe to eat, once you remove the affected area. 

I hope this is helpful! 

Do you have a picture of the orange in question? That would help greatly with diagnosis.