Without being able to actually examine this particular sari, it looks to me like they have sewn a plain gold ribbon to the right side edge with the stitching going down the centre of the ribbon, then turned the ribbon to the wrong side and stitched it down so that half of the ribbon is behind the blue fabric and the other half sticking out from the edge, which now has the raw edge concealed.
Hard to explain but I hope you get it.

Colleen, you may be right, but my first thought was that a narrow hemming foot was used on the purple and then just stitched it onto a wide gold ribbon (about 1.5 inches) at that spot shown. This way, the sparkly would still show through the purple as in the photo. Many gold trims would not be sparkly on both sides, as would be necessary in your scenario. Either method would work if you found the right trim.

Hi Donna, the gold trim wouldn't need to be sparkly on both sides if the trim was sewn on right sides together before flipping it to the back.

That would work, as long as the trim was at least 2 to 2 and a half inches wide.

Oh no, I think you meant wrong sides together, so that the sparkly is on both sides, right?

No, right sides together, sew along the edge, turn from the seam (halfway, not all the way), now the ribbon is sticking out and the raw fabric edge is turned under. Topstitch to hold it down (or carefully handsew from the back).

Right, I gotcha. Yes, that would work and would also give it some body, with the double thickness.

Would a ribbon hem work? Here are directions for that - it's the way I was taught back in the day @ F.I.T....

How to Sew a Ribbon Hem

That's pretty much how I meant, except that for the effect the OP wants you'd sew the ribbon onto the right side of the fabric and also sew down the middle of the ribbon so that some is left sticking out and the rest is under the fabric as seen from the finished right side.