The Icelandic Highway Authority (Vegagerðin) classifies all its roads into different hierarchical groups;
Stofnvegur (S) - literally translated to main road, i.e., primary road or trunk way (route 1),
Stofnvegur um hálendi (Sx) - main road over the highlands,
Tengivegur (T) - connecting road, i.e., secondary road,
Héraðsvegur (H) - county road, and
Landsvegur (L) - country road, often used for all other roads that don't fit in the aforementioned categories.

The road classifications can be found in Vegaskrá, which is a public document and can be used according to https://wiki.openstreetmap.org/wiki/Iceland .
In Vegaskrá you can find the classification under "Vegflokkur".

I don't really know why designation is used. According to https://wiki.openstreetmap.org/wiki/Is:Map_Features , the tag "network" should be used to indicate the road classification. I have simply been following convention seen on other roads.