These documents generally refer to medical decision-making, especially end-of-life decisions. The document name sometimes varies by state, which is why there are so many terms. In California, it’s usually called an “Advance Healthcare Directive”, which generally means the same thing as a “living will” or a “power of attorney for healthcare”.
Whatever its name, this is a document that you use to tell others what to do if you are unable to make your own medical decisions, tells them under what circumstances (if any) you would wish to be removed from artificial life support, and appoints a person you have selected to consent to (or withhold consent from) medical procedures when you are unable to do so.
It is a critically important document to have. There have been many cases in the news of family members battling in the courts over whether or not a loved one should be kept on life support or allowed to pass comfortably. One such well known case was that of Terry Schiavo in Florida.
You can download a form to use for this purpose at the California Attorney General website.