The illnesses covered under the policies vary. Policies typically insure for certain forms of cancer, heart disease and stroke, but some cover a far longer list of ailments, including coma, paralysis, Alzheimer's, multiple sclerosis and loss of hearing. (Certain conditions, such as benign tumors, may not be covered in all policies.)
The policies provide lump-sum payments that can be used to cover many costs related to illness -- including copayments, travel expenses, experimental treatments or wages of a family member leaving work to help -- that often aren't covered by health or disability insurance.
This idea, which I call event-driven insurance, has a number of merits. It is genuine insurance, in that it covers large risks. It does not reward doctors for ordering procedures. It does not require you to submit detailed bills in order to collect claims, thus saving on administrative costs.