an Authoritative answer would only come an NS which has been configured to be incharge of the domain, while a non Authoritative answer would come from the rest of the NSs in the world. an answer that they recieved after asking somebody else or using their cache and are forwarding it to you, not an answer that they are responsible for.
Its basicly the NS telling you "hey, im not incharge of this domain so the information im giving you is second hand... if anything is wrong, dont shoot the delivery boy"
