Discussion on: What programming best practice do you disagree with?

I've never fully understood getters and setters. If I have a field that has both a getter and a setter like so:

class Person {
   private String name;

   public String getName() {
     return this.name;
   }

   public void setName(String name) {
     this.name = name;
   }
}

Why not just make the field public? What's the point in making getters and setters and not just dealing with the field directly? I asked one instructor about this and he just said "it's better encapsulation" but I don't see it.