An AS (identified by an ASN) is an autonomous system. It's comprised of multiple CIDR blocks, contiguous regions of IP addresses. The network definition (by CIDR block) is fairly dynamic, as blocks can be added, deleted, or consolidated.
An autonomous system is a single administrative domain over public IP space. Essentially, autonomous systems are what the Internet is inter-networking between, through BGP (border gateway protocol). BGP and AS are what Cisco (and other router) gear are ultimately all about.
So yes: organisations typically have one AS. Exceptions are typically the result of corporate mergers (not uncommon) or government space (where the domains are large).
(Disclaimer: I'm not a networking bithead, don't muck with routers much, and have a rough knowledge of much of this, though it should be vaguely accurate.)