A top-level network on the Internet.  There are 16 Tier 1 networks worldwide.  In the U.S., AT&T, CenturyLink, GTT, Verizon and the Zayo Group are Tier 1.  Germany, U.K, France, Hong Kong, Japan, India, Italy, Spain and Sweden host the non-U.S. networks.
Known as "settlement-free peering," Tier 1 networks are private networks that allow traffic from other Tier 1 networks to transit their backbones without a fee.  See 
peering and 
IXP.
Tier 2 and Tier 3 Networks
Tier 2 networks peer with some networks without fees but pay to reach a large portion of the Internet.  Tier 3 networks always pay fees to obtain access to the larger backbones.
ARPAnet to NSFnet to Tier 1
ARPAnet was the original Internet backbone, which was superseded by the National Science Foundation Network (NSFnet) in the late 1980s.  NSFnet was replaced by Tier 1 networks in the mid-1990s when the Internet became a commercial venture.  See 
ARPAnet, 
NSFnet and 
Internet.