As can happen with many different stitches and embroidery techniques, there are different ways to execute a stitch. This can depend on the country where it is being done, or in the case of Italy: the region or even the town. Some associate the Gigliuccio's origins with Tuscany where it is the traditional edging of Punto Antico which some also associate with Tuscany, but in truth it is done all over Italy.
Some call the Gigliuccio the Fleur des lys stitch and associate it with Florence and the lily. Some associate it with the Gigliucci family of Fermo, Italy where it is said there is evidence of the stitch as far back as the end of the 1600s. We might be safe to say it is definitely an Italian stitch from the region that became Italy in the late 1800s – because technically Italy was not officially "Italy" before the Unification. I say 'might' because when I did finally find something that looked like the Gigliuccio I'd seen in RAKAM, it was in a Schwalm book by Renate Fernau and it was called the Peahole Hemstitch.
If you don't care too much about where it came from, then we can move on to what it is, because here, more or less most people are in agreement. More or less. ;-)
Basically it is a Drawn-Thread technique consisting of groups of knotted bundles in an open channel between two rows of Four-Sided Stitch, also known as Italian Hemstitch. There is a tutorial for executing it on the right side of the fabric here, and a two-part tutorial for using it to secure a hem, executing it on the back side of the work starting here and ending here.
There are many different ways to execute the Gigliuccio hemstitch, you will need to try a couple different ones (I'm sure there are other methods that I haven't yet discovered) to see which one you like best, regardless of the technique used to make it, the result is a beautiful openwork channel which plays with the effects of chiaroscuro and is very pleasing to the eye.
It can be done in tone-on-tone, in light-coloured thread on dark fabric or dark-coloured thread on light fabric: each gives a different effect. Done in multiple rows at a hemline, or in a single row to connect the motifs of a tablecloth, or however else you can imagine it, it is always attractive. Do a Google image search for some inspirational photos!