The questioner may be referring to the 2 containers (box within a box) for the shel-yad bayit (the shel rosh only has one)
Shalom, Thank you for your comments. Of course, now that you mention it, the question may very well have been asking about the extra covering that some people have on the arm tefillen. This extra covering is purely to keep the tefillen in good shape, and is not required at all. In fact, some opinions like to keep the tefillin open so that they can be touched during the prayer service. In order to facilitate this, I have seen a smaller cover for the arm tefillen that only covers the very top edges of the tefillen box. But even this smaller cover is purely optional – and to the best of my knowledge all types of extra covers for the arm tefillin are a fairly new practice. Blessings.