Dave is correct, it is oilcloth, it has a glossy finish and a fabric backing. It is still available at select stores. It is long lasting but hot pads are needed when placing hot pots on it. It is also prone to being ripped or snagged. Its purpose was to protect table tops which in those days were mostly wood. After a time, the table top varnish could become embedded with fuzz from the fabric backing, but the smell of fresh oilcloth has a pleasant smell which most kids remember long into adulthood.

I was looking up Dennison in Framingham for a project and found this picture. In my search, I had already come across the following, which exactly describes the activity here:

"By the 1920s, the company was making paper tags with reinforced holes," says company president George Phelps. "But there were no automatic wiring and stringing machines. Back in those days, people in town took the tags home and attached strings or wires in the evenings to make some extra money. They were collected in the mornings."

Dennison was a label making company. They were bought by Avery in 1990 and are today Avery Dennison http://www.avery.com/

They made all sorts of labels for offices, shipping, schools, libraries, etc.

What kind of tags are they working on? They almost look like shipping labels.