It's one of those ubiquitous Turkish/Ottoman rugs that you see in almost all of his English portraits. So ubiquitous, in fact, that if you search ArtSTOR for "Holbein", about a hundred of the extant rugs show up.

They were a prestige item all through the 15th and 16th centuries. One of my professors insists that there's a further connotation to them that deals with Christianity triumphing over the "heathen" Islamic culture that produced them, which is why they were so popular to put under the likes of the Madonna in 15th c. Flemish and Burgundian artwork. I'm not sure I totally agree, but for sure by the time the English nobility were being painted by Holbein, they were basically a luxury good, signifying wealth.

I seriously think we need to get a costume group together and do a shoot at the Frick. It would be EPIC.

As the eminent sarahbellem says, its a turkey carpet.

Way too expensive to walk on, so they were laid on tables where they are seen in all their beauty.

We have a few threadbare ones in Kentwell!