OMG!
I haven't seen that stuff in about thirty years.
It was put up with adhesive, and it was the lowest-cost option for people who couldn't afford real tile, which was a lot of people in the '50s and early '60s. I remember it in kitchens and bathrooms. It worked out decently well in kitchens, pretty much, but you had to be pretty desperate to use it in a bath, because it was so prone to water damage around tubs.
After this stuff came melamine tileboard, which was Masonite faced with a couple of microns' worth of melamine. It had a tile design pressed into it. It looked okay new, but as soon as the melamine got scratched, the Masonite started getting wet and rotting.
Then came plastic tile, which was a decent enough solution as long as it was over the same concrete backing as was used for ceramic tile. Trouble was, that concrete backing represented the major portion of a tile job's cost, so plastic tile didn't save you much money, if properly installed. Many people just glued plastic tile up themselves, over wallboard, with predictable results.
Last was ceramic tile, which was the only thing that really held up back in the day. Today, prefab plastic tub surrounds are watertight, hold up for years, and have nothing to rot. They're at a lot of different price points, too. But back then, your Aunt Dixie (and my grandmother) didn't have a lot of options.