How can I refinish a basement concrete floor?
Those aren't sub layers. I would say those are actually just layers of paint. The mesh could be left over from a carpet that was once there. Potentially, that's the glue mixed with the carpet mesh that didn't get removed when they removed the carpet.

Refinishing would require you to sand that baby down, and choose what you want to paint over it. Latex paint should work fine. For a stronger and more durable layer on the floor, I would go with an industrial epoxy finish. NOT THE KIT. Heard bad things about the kit and about how they don't last. 

Latex paint will get you what you want if you're just looking to hide those imperfections. Choose a flat paint and don't forget to prime it all first.