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I have two of what looks like the chair version of that sofa that I found at an antique store. They are very comfortable and good quality.

High density foam is a yellowish foam that is used in a lot of furniture cushions and in things like egg crate pads for sleeping. I assume he just means that the cushions aren't stuffed with down (like old Eames lounges were) or horse hair (like early mdernist furniture was).

High density foam is less porous than other industrial foam products like sponges or florist foam. Thus, it is somewhat water resistant and is less likely to absorb spilled liquids or sweat (yeah, I know kinda gross).

These can be very neat and fun pieces -- you'll need to watch out for deterioration around the edges/curve (any feeling of crumbling or softness) and sometimes the cushions on these sort of harden and get funky (become solid and crumbly). If the edges are in good shape, the cushions can be replaced, I think, though not with identical materials.

Could he mean "styrofoam?" I know LL Bean carries "ultra-lightweight" furniture that features "molded polystyrene frame" construction.

That sofa, and others like it, such as Arne Jacobsen's "Swan Chair" and Saarinen's "Womb Chair" are made with what's called "cold foam" and if you want to re-upholster, the foam must be replaced as well, because it's stuck to the outer finish material.
A place called Thomas Amato in Tribeca did a good job for me but it wasn't cheap.

urbanista, I think you're confusing open-cell and closed-cell foam. Chances are these are made out of closed-cell foam, which means they could be very rigid (think: styrofoam) and completely waterproof (think: neoprene).

there is also polyurethane foam which is rigid and intended for exterior applications. i'm not sure what he means by "high density".

I believe Ligne Roset's Togo Sofas have been using different densities of foam for a long time. My mom has an old old old set she bought about 20 years ago and it's still comfy and hasn't been beaten down into powder -- quite a feat for a sofa made entirely of foam.

These are Overman couches - from Sweden. I've had three of these in the past and a chair and all were in good condition (and comfortable.) I've never had one with rotten foam. They hold up much better than the old Knoll pieces. The foam is firm but not uncomfortable. The fabric usually goes before the foam. Ask the seller if you can see them before committing to buy - then sit on them and check it out for yourself. Good luck!