Rather than write an answer from scratch, I?ll refer you to an old, but accurate, Network World article.
In a nutshell, Tier 1 providers have their own coast-to-coast backbone. They also have peering relationships with most of the other Tier 1 providers. Tier 2 providers get access from Tier 1 providers, but they usually have to pay for the access (which is different from the free "peering" relationships Tier 1 providers have). Tier 3 providers generally specialize in a regional presence.
This was first published in May 2002