An Authoritative DNS server is a DNS Server which holds the Zone for the DNS Namespace domain and holds the original Resource Records for that domain. Authoritative DNS servers are the original source of the information for name resolution of the DNS Namespace domain which it holds. Authoritative DNS servers are the final source of information for name resolution for the DNS Zone it holds.
A Recursive DNS Server is a DNS Server that answers queries to an end DNS Client by sending DNS queries to other Name Servers. A Recursive DNS Server traverses the DNS Namespace tree with Iterative DNS Queries from the highest Root level to lowest Authoritative DNS Server, until it finds the answer for the Recursive Query from its DNS Client.
Click the following link to learn how Recursive and Iterative DNS Query works.