That's sooty mold. It occurs on fruit and on leaves. It is caused by aphids, scale, or some other insect that leaves a sugary film on the fruit or foliage. This sugary solution is then consumed by mold that results in the black film.

It's not dangerous just unsightly.

Sorry my English skills seem weak this morning. Maybe you can understand what I mean.

Hello from Michigan Elisa,
Where would you be located? I am interested to know if these apples are fine and good for picking (besides the soot) here in early December - or are they from storage?. If so, that's a nice tree!
Jim

Fruitnut -- your English is perfect and I thank you very much for your informative answer! So, I will make apple sauce with no regrets.

Jim, I am in the mountains of West Virginia, and the apples were indeed picked in mid October -- it is only now that I'm realizing that eating them one at a time will not use them all up fast enough, and so into the apple sauce pot they go.

Elisa, yellow apples tend to be very susceptible to a fungus called sooty blotch which has nothing to do with aphids. In humid parts of the country this is more likely to be the issue than aphids, but same difference as it is completely harmless and is only a cosmetic problem.

If you are curious you can find a picture of the disease on-line without much effort now that you know the name.

Harvestman -- I did check the photos, and honestly can't tell if it's sooty mold or sooty blotch, but great to know either one is harmless.
Thanks!