Well there are actually two kinds of proxys also know as durable power of attorney. One like your grandmother has asked you to be is a healthcare proxy. That is that in the event that she is unable to make decisions for herself coherently, the proxy will be the one to make those decions for her concerning her health care. It is important that you know what the person you are representing would want and it would require that you be involved and know what is going on with that person. I would recommend going to a medical examination with them so you can have an idea and see the doctors as well as the person you would represent views of their particular situation.
The other proxy or durable power of attorney is concerned with financial matters. As in the case with the healthcare proxy in the event that the person like your grandmother is unable to coherently make decisions for herself the financial proxy would make decisions for them regarding their finances.
In all cases of a proxy the proxy should be someone that is trusted and able to make hard decisions for the other person. The wishes of the person should be documented and who the proxy will be should also be documented, signed, and witnessed with copies made and distributed. Also note that in the case that the person got better and was able to coherently make decisions for themselves the proxy would no longer be in effect.