IMHFO it looks to me like the backing off the vinyl & glue on the floor to adhere the vinyl to the underlayment {underlayment is a thin layer of high density particle board 1/4-3/8-1/2" thick, nailed down over the sub-flooring, that's usually used under the vinyl covering, for a smoother floor, that they put a water base mastic glue on (unless it's over 25 y/o), before rolling on the final vinyl covering, some people refer to as Linoleum, that had asbestos fibers, was an oil based product & is really hard stuff, not soft like vinyl}, a big scraper & elbow grease, usually they have an underlayment under vinyl to make the surface flat, nailed & even glued sometimes, on top of whatever is under that, if it hardwood under the underlayment, you could just pull up the underlayment in pieces, score it with a skill saw, just set the saw depth so it doesn't go all the way thru, then pop up the boards, they usually would use ring shank nails too to put down underlayment, they can be a real PITA to get out too... That's the way most floors are put down anyway, not 100% sure how yours was done, but that's the correct way to install most flooring... Good luck... what are you planning on putting down, instead of the vinyl ??
