Most all mattresses use poly foam (made from polyurethane) to cushion their beds. Even expensive brands like Tempurpedic will use this foam in the base and side rails. Polyurethane foam is fairly light which helps when making a lighter weight mattress. Polyurethane foam can come in many different densities and its quality can very quite a bit.
Polyurethane resistant to body impressions, which why it is such a popular component of most beds. Even higher end mattress brands use polyurethane to enhance the sleep surface comfort of their mattresses. It helps mattresses keep their shape longer, as well as doubling over as an allergy-friendly bed component.
The problem with poly foam is that it can have a distinct smell and is the reason for most off-gassing. Also, look out for when polyurethane foam becomes old. It can begin to crumble and tear easily.