return this.User.compareTo(arg0.User);
When you write this line, you compare the User object and return the result.
Comes this, which points to the current instance, when you pass the "Other" to this method, it is called in the current instance, which is compared with the passed objects User.
If you see the signature
public class Other implements Comparable<Other>{
public String User;
String, User.
, .
:
Collections, , , . .