Abstraction is hiding details of specific implementations and share common details among implementations. Example is java.util.List, java.util.ArrayList and java.util.Map. List is the parent (the abstraction), ArrayList and Map are specific implementation.
You want to do this whenever you have shared code between different classes, so that you don't repeat your code which is bad.
Abstraction is very useful in code reuse, dynamic behavior and standardization. For example, there is a method that you are using and it accepts a List, so to use this method, you can send any object that has list as its parent. Now inside this method, there could be different implementations depending on what is the type of the passed object, so you can achieve a dynamic behavior at run-time. This is very useful technique when you design a framework.