What she's calling perimeter fabric, and what I'd call "background" fabric, is two pieces, a top and a bottom. She sews the top half of the sewn together death star to the top perimeter or background piece, and then sews the sewn together bottom half of the death star to the bottom perimeter fabric. If you zoom in on the photo you can see the seam (it curves) of the top and bottom perimeter fabric where it's joined. That's why she leaves the bottom portion of the top half and the top portion of the bottom half of the pieced death star unsewn and clips the curves, so that she can then sew the whole thing together.
At least this is what I think she means. Clear as mud?
What I wonder if why she didn't sew the top half of the death star to the bottom half and then applique the whole thing to the perimeter or background fabric. Wouldn't it have been easier? Or maybe I don't "get" it, after all.
I'll look now to see how others interpreted this.....and may then delete my own post, if I have it wrong!