What is this dry skin on my achilles tendon and heel?

I don't know.: It could be an irritant or allergic reaction due to clothing or shoes or exercise; or it could be an unusual presentation of athlete's foot; or it could simply be dry skin. Someone (preferably a dermatologist) will need to physically look at it to give you a more precise answer.

Possible fungus: Dry cracked heels could be a sign of a fungal infection. Other causes include constantly wearing open heeled shoes. You can try otc Lamisil (terbinafine) cream twice a day. A skin culture may be helpful if it doesn't improve with otc meds.