Basically your cells need scaffolding to build on. If the scaffolding is still there, like from a minor cut or burn, then the cells around it will fill the area back in and completely heal it. When you get to a more major cut or burn, that's kind of how scar tissue comes around. The body is desperately trying to fill those holes back in, but it get's kind of disordered and the filling ends up looking different than the original. The scaffolding is very far apart, but it can still be filled - it's just kind of ugly. When you lose like a finger - there's absolutely no scaffolding. It's gone. It left with the finger. The cells fill back in the areas they can where there is some distant edges of scaffolding, but they can't grow up or out. There's just nothing to hold on to.

If this wasn't the way tissue worked, cancer would be a lot more common. One of the principle characteristics of cancer cells is that they will grow up and out. This leads to uncontrolled growth, tumors, metastases, etc.