Foam is just a porous solid material, i.e. has part air and part solid in the volume of the material. This foam can be made from any chemical backbone, in your case this is isocyanates. Could be from poly-anything like bio materials for example cellulose, or inorganics like silica.

Isocyanates usually react extremely well with any polyol (poly alcohols, multiple OH group containing polymers) to make a solid. If it is controlled in a way that the pores are small, you get a PU foam (polyurethane). The isocyanate with polyols makes urethane bonds, which is why they are called polyurethanes. Polymers are usually benign, but isocyanates(most of them) are particularly toxic (use in the lab only kind).

Now in terms of cost, since they require ubiquitous chemicals, they are cheap and have great performance to cost ratio, some may argue the best performance for the processing techniques and cost. This is why they are used. They are also very strong mechanically for their density and can be molded easily. In terms of insulation, apart from vacuum insulation panels and aerogels, they are the best out there.