It means that your parents can grant you certain rights that an adult would have by outlining those rights in a formal document. This is a non-judicial process, and is the successor to emancipation by notarial act.
They cannot grant you rights where the grant would conflict with state law -- an obvious example would be that they cannot give you the right to buy alcohol -- and that's something that you would have to research in specific relation to any given right that is granted in the document. I doubt that you're going to find a list of all rights that are excluded from that provision. For example, you might find that the DMV won't accept the document in lieu of your mother's signature; that's not something I've researched, but it is something you should explore if your hope is to use the document to avoid her having to sign documents with the DMV.
Note also that even with emancipation, no apartment has to rent to you at the age of 16 or 17.

