WordNet
n. an interest in a person or thing that will support the issuance of an insurance policy; an interest in the survival of the insured or in the preservation of the thing that is insured
Wikipedia
Insurable interest exists when an insured person derives a financial or other kind of benefit from the continuous existence, without impairment or damage, of the insured object (or in the case of a person, their continued survival). A person has an insurable interest in something when loss of or damage to that thing would cause the person to suffer a financial or other kind of loss.
Typically, insurable interest is established by ownership, possession, or direct relationship. For example, people have insurable interests in their own homes and vehicles, but not in their neighbors' homes and vehicles, and certainly not those of strangers.
The "factual expectancy test" and "legal interest test" are the two major concepts of insurable interest.