Why do African baby elephants hold onto their moms tail?

Because, like all mammals. Elephant calves are helpless by themselves when they are born. They are pretty much like human kids who are entirely dependent on their parents for their survival. So they stay with their mother and her herd so that the elders can protect them and teach them how to survive. The lessons learnt by baby elephants from their mother and herd helps them survive for the rest of their life.