Why do my toenails have callous/flesh attached?

This is a disgusting question, I know, I'm sorry. When I cut my toenails, the outside curve is normal, and the inside curve has some sort of thick callous along it. I tried looking it up and I found a lot about ingrown toenails...I know for a fact that I have none of those. Can you help? What are they and how do I get rid of them?