An Enduring Power of Attorney is an appointed person or legal entity who has the power to manage your financial and legal affairs during your life, and unlike an ordinary or limited power of attorney, can continue to manage these personal affairs when you lose the capacity to do so yourself.
Matters that an attorney might deal with are paying your bills and taxes, signing legal documents, handling property etc. and an enduring power of attorney in particular provides for circumstances in which a person has lost the mental capacity to conduct their own affairs, so is especially important for elderly people.
An enduring power of attorney registered in any state in Australia is automatically recognised in other states, although each state has different laws regulating power of attorney. A power of attorney however is not recognised in Australia when it has been made overseas.
A power of attorney terminates upon the death of the person, their Will (and executor of their Will) takes over to ensure that their assets will be taken care of and distributed according to their wishes.
It is important to have both an enduring power of attorney and a will.