| In general, a power of attorney is a document which, when signed and made legal under the laws of your location, allows someone else to act in your behalf. This person is your "agent" or "attorney-in-fact" (though they don't have to be a lawyer). A power of attorney is often used as a preparation in case a person becomes incapacitated and unable to make their own decisions, and nine9 reminded me that one is sometimes used when a person plans to be outside the country they live in for an extended period of time. A set-up where the power of attorney doesn't go into effect until the person granting it becomes incapacitated is called a "springing" power of attorney, because it "springs" into effect at a certain time.
The standard Durable Power of Attorney (so called because it lasts until you die, revoke it, or for some reason a court declares it invalid) gives the agent power over a person's finances. Without a Durable Power of Attorney made in advance, it is often necessary to go to court for family members to get the power to make financial decisions for the person who can't do it for him/herself.
The standard Durable Power of Attorney does not give the agent power to make medical decisions for the incapacitated person, but many jurisdictions have a Health Power of Attorney, where you can appoint someone to make health decisions for you if you can't. This would usually be stated in an advance directive along with any living will type instructions on what treatment you should receive. | 
