Autonomous System Check
An Autonomous System (AS) is a group of IP networks run by one or more network operators with a single clearly defined routing policy. Each Autonomous system is identified by a 16bit or 32 bit ASN number (ASN) and is assigned to a regional registry, an internet service provider or a company who is responsible for routing and administration of these network ranges. Simplified, you may think of this company or organization as the owner of the AS networks assigned to them.
Knowing the ASN of an IP address is important because in the case of routing problems or IP abuse, you know who is responsible and should be approached for remediation. The ASN and the name of the responsible organization is shown in the IP Checker results as IP Network Owner.
References
Autonomous system (Wikipedia)