What is the thin little border next to a big border called?
 

OK...I know you are thinking I am off my rocker...well I am thinking it too!! ha ha

I can not think of a name for this process....putting a thin (approx.) 1/4" folded fabric next to a border in a quilt. It isn't sewn down...you attach it to the border then sew the border and this ( )piece to the quilt. it is like a flap.

OK can you help my tired brain?

Is it a flange?

YES!!!! Thank YOU SO MUCH!!!

Piping maybe?? Flange maybe?? :):p

Yep, flange.

Flange if it's flat, piping if it's stuffed.

It's a flange. Also heard it called a crumb catcher and a flipper flopper......we like to name things silly in Minnesota!

And, what is the purpose of this the flange? I am not familiar with the term but, then I haven't been quilting very long either.

It is just a different little extra in the border of a quilt. Some folks like them, some don't.

Usually a flange as it flaps. But you can place a very narrow border in a quilt either in the binding ie flange flap or between sections.
I put flanges by my borders but find it easier to cut 1" strip fold. In half and put around edge and then bind in normal way. I find I am not capable of stitching exactly on the right place and machine line, flange anD binding always looks a mess. The way I do it no problem. I have wondered if you could cheat with a narrow border by using sticky celtic knot binding and sewing that where ever you want.