What is power of attorny ?

In general, it is, as Google says, "the authority to act for another person in specified or all legal or financial matters."

There are differing types, and that kinda depends on what it's being used for, e. g. investments, health care proxies and the like. But the generalized term more or less means to act for someone else in what are often rather big decisions.

What is health care proxies ?

They vary from state to state but the general idea is that it's a document allowing someone to make medical decisions for another person.

It is basically a legally written document in which one person (the principal) appoints another person to act as an agent on his or her behalf.

A power of attorney (POA) is a document that allows you to appoint a person or organization to manage your affairs if you become unable to do so. However, all each type gives your attorney-in-fact (the person who will be making decisions on your behalf) a different level of control.