In legal terms, if someone dies without having made a will, they're intestate. Your great aunt may have intended to leave all her money to her cats, but unfortunately for Flufferkins and Mr. Wiggles, she died intestate.
Like a lot of legal words, it might seem more straightforward to simply say, "without a will," but lawyers like to use Latin whenever possible. Intestate comes from the Latin intestatus, "without a will," from the root testari, "bear witness," which it shares with testament. When someone with a lot of money or property dies intestate, it can complicate things for the relatives they leave behind — it's not clear who gets what.