A power of attorney proves to other people that your attorney has the legal authority to look after your legal and financial matters. Without it, other people may not accept that your attorney can do these things on your behalf. It becomes important if you are travelling or just not physically present to sign documents or otherwise deal with your legal and financial matters.
These days the power of attorney is becoming less important in New South Wales because of the way that business and other transactions are conducted. For example, electronic and internet banking now means you can potentially access your bank accounts from anywhere in the world and do your own banking, even property transactions are moving towards electronic dealings which do not require original signatures. In many cases, there are more practical alternatives to the power of attorney, but in the absence of any other authority, the power of attorney would be the overarching legal authority.