The page about this tapestry has a full description, including the story of Veronica's veil and lovely close-up photos.
In style and execution and age, it looks very like the one I was lucky enough to work a year ago.
I highly recommend that you visit the Met's posting, particularly to look at the detail photos. I find myself so intrigued by the faces and expressions of the people. They are so sensitive and so clearly portrayed as distinct individuals.
The technique and skill needed to produce that effect is amazing to me. They were (and tapestries still are) woven on vertical looms. These old ones were huge pieces (the one at the Met is over 11 feet square). They were mounted on the looms sideways, i.e. with the top and bottom of the scene at right and left, the side edges of the scene at bottom and top. There was an outline drawing of the design, known as a cartoon, mounted behind the loom to guide the weaving. Seems to me to be amazing detailing by people seeing only a small portion of the piece at a time, and having a sideways view of it at that.
The description of my tapestry adventure can be found at these posts: one, two, three. Here's a detail of that tapestry. I would love to know what these two are talking about!
Checking in with the Artwork of the Day sounds like a nice way to get a good day started, doesn't it?