An Autonomous System (AS) is a group of IP networks run by one or more network operators with a single, clearly defined routing policy.
When exchanging exterior routing information, each AS is identified by a unique number: the Autonomous System Number (ASN). An AS is also sometimes referred to as a routing domain.
Current RIPE Policy requires a network to be multi-homed, and have a unique routing policy for an ASN to be assigned. Requests must show the routing policy of the AS.
Any organisation can acquire an ASN. This requires a contractual agreement with a sponsoring LIR or with the RIPE NCC.
Do you speak Russian? We have a summary document that explains how to get IPv4, IPv6 and ASNS from the RIPE NCC in Russian: Getting Resources (Russian).