Showing the description for the term identified by the argument in the Taxonomy Term view
I want the description for the term coming in via the contextual
  filter argument


Ok then, 

1) Create a new view


Show: Taxonomy Terms. 
☑ Create a Block


Display format: Unformated list of Fields



2) Save and Continue.


Add the Contextual Filter.
Add the description field.


3) Go back to your other view and attach view to header.