A tier 2 network is an Internet service provider which engages in the practice of peering with other networks, but which also purchases IP transit to reach some portion of the Internet.
Tier 2 providers are the most common Internet service providers as it is much easier to purchase transit from a Tier 1 network than it is to peer with them and attempt becoming a tier 1 carrier.
The term tier 3 is sometimes also used to describe networks who solely purchase IP transit from other networks to reach the Internet.
The ASxxx refer to each network's IANA-assigned AS number.