AS numbers is part of the BGP protocol, when you are a large organization with multiple presence points on the internet you need to advertize your prefixes (routes), i.e. the IP blocks that you host behind your routers, and to do that you need to be an "Autonomous System" and to be one you need to register with IANA (it costs $500 I think and you need to prove that you actually need one) and you get an AS number. The techincal details are here: https://tools.ietf.org/html/rfc4271