In the purest sense, non-toxic can mean foam that is made out of all-natural ingredients. This often leads to labels like "organic foam." Some versions of high-density foam, for example, are made with soy products. These do not have the same durability as normal foam, but they can help satisfy customers who are looking for a fully natural and non-toxic option. Latex foam is another all-natural option.
VOCs are volatile organic compounds, the primary culprits in toxic foam that are released into the air and then breathed in. This is where the non-toxic definition becomes tricky. Some companies sell non-toxic high-density foam that is made with plastics like urethane derivatives, but provide the non-toxic label because the VOC count is low, or it has no known carcinogens. Sometimes non-toxic can mean the factory used a foam blowing technique low in toxic chemicals.
The problem with this strange mix of non-toxic labels and high-density foam made out of plastic materials is that under the right conditions, the plastics can be toxic. This is especially true of flammable high-density foam. If the foam material catches fire, it will produce highly toxic exhaust. While it isn't an everyday concern, it is a toxic factor in many "non-toxic" materials.
There are also wraps that you can use around high-density foam in order to give it all-natural and non-toxic properties. If you want to buy a high-density foam, you may be able to choose an inexpensive foam but also purchase a wool wrap made out of fully natural, non-toxic materials to encase the foam.