A Tier 2 Network is an Internet service provider who engages in the practice of peering with other networks, but who still purchases IP transit to reach some portion of the Internet.
Tier 2 providers are the most common providers on the Internet as it is much easier to purchase transit from a Tier 1 network than it is to peer with them and then attempt to push into becoming a Tier 1 carrier.
The term Tier 3 is sometimes also used to describe networks who solely purchase IP transit from other networks (typically Tier 2 networks) to reach the Internet. The majority of Tier 3 networks are usually single rather than multi-homed and therefore are vulnerable to depeering disputes.