Autonomous System (AS) is a collection of IP prefixes with a defined routing policy with other systems. Each AS must have a unique number or ID that allows it to communicate with other systems. This identifier is called the Autonomous System Number (ASN).
ASN can be private or public, where public ASNs are used to exchange info over the Internet, while private ASNs are used to communicate with individual providers through Border Gateway Protocol (BGP).
ASNs are assigned by the Internet Assigned Numbers Authority (IANA). You can see the ASN summary for the United States here for instance.