I am having difficulty finding a translation for this word. It is in the context of weaving small, checked (plaid in Am. English) cloths. The other two types mentioned are Hälskläden (necker chiefs, I think) and Huvuddukar (head coverings?). The weaving book is in Swedish.
Förningsdukar is the plural
Förningsdukar is the plural of förningsduk, which is a like a small tablecloth.. I found this explanation in English.http://www.vaxbolin.se/product/fornings/?lang=en
Halskläde is, as you say, a neckerchief.. or a square type scarf that's folded into a triangle to be worn. Not a word I've heard recently unless it's referring to traditional dress. Huvuduk is a head covering, huvudukar being the plurar.
All could be small square plaid weavings
föra (verb) = bring
förning (subst*) = what you bring, in the case of förningsdukar: "eatables" you brought, either to the party (is that what is called potluck?) or, in some parts of Swe, eatables you brought to/for the family at the "party house" - a cheese, fo example.
Thus, a förningsduk was used as furoshiki... so many different cultures share the same ideas.
* Edit: oops, it is called noun in English...
Here's a trick -- search at
Here's a trick -- search at google.se instead of google.com and then translate the page. Or go to the images tab and look at the pictures, which may give you enough hints to figure something out.