An autonomous system (AS) is a collection of connected Internet Protocol (IP) routing prefixes under the control of one or more network operators on behalf of a single administrative entity or domain that presents a common, clearly defined routing policy to the internet.
Originally the definition required control by a single entity, typically an Internet service provider (ISP) or a very large organization with independent connections to multiple networks, that adhered to a single and clearly defined routing policy, as originally defined in RFC 1771. The newer definition in RFC 1930 came into use because multiple organizations can run Border Gateway Protocol (BGP) using private AS numbers to an ISP that connects all those organizations to the internet.
Even though there may be multiple autonomous systems supported by the ISP, the internet only sees the routing policy of the ISP. That ISP must have an officially registered autonomous system number (ASN).
A unique ASN is allocated to each AS for use in BGP routing. ASNs are important because the ASN uniquely identifies each network on the Internet.