In my experience whenever I am using a subsurface modifier this happens. It is important to add geometry. More specifically though, the reason the box appears this way is because you have not applied the modifiers... Therefore, it is showing you two things

1. What you mesh looks like whilst you have the modifier set but not applied.
2. The original mesh points which can be seen because you haven't yet applied the modifier.

All you need to do is tab into object mode, select the modifier and apply them. You can do this by clicking 'CTRL A'. Once the modifier is applied you will be able to edit directly on the mesh.

Hope that helps :)

In my experience whenever I am using a subsurface modifier this happens. It is important to add geometry. More specifically though, the reason the box appears this way is because you have not applied the modifiers... Therefore, it is showing you two things

1. What you mesh looks like whilst you have the modifier set but not applied.
2. The original mesh points which can be seen because you haven't yet applied the modifier.

All you need to do is tab into object mode, select the modifier and apply them. You can do this by clicking Ctrl + A. Once the modifier is applied you will be able to edit directly on the mesh.