What it means
Intestacy is what happens when a person dies without a valid will. Each Australian state and territory has its own statutory formula that decides who inherits — usually starting with a spouse or de facto partner and children, then moving to other relatives. Because the formula is fixed, it takes no account of your actual relationships or intentions, and people you may have wanted to provide for (such as stepchildren or close friends) can miss out entirely.
How it's used
Because their father died intestate, the family had to apply to the Supreme Court for letters of administration before they could deal with his estate.