What is this driver-related attachment?
I believe the component you have is defective. I have what I believe is the same set of tools, and is the same brand name.

It is an extension for the main handle.



I am unable to separate the hexagonal portion from the black cylinder. The joined area of my tool appears to have epoxy or similar material bonding the two pieces together.

I would not have expected epoxy as the only bonding material, although I have yet to over-torque anything and have the bond break.

If you are able to insert the cylinder end on the hexagonal portion and engage some of the hex portion of the cylinder, you too can epoxy them together and have a working tool again.

EDIT: added two photos by request.