A relationship between two or more small- or medium-sized ISPs in which the ISPs create a direct link between each other and agree to forward each other's packets directly across this link instead of using the standard Internet backbone. For example, suppose a client of ISP X wants to access a web site hosted by ISP Y. If X and Y have a peering relationship, the HTTP packets will travel directly between the two ISPs. In general, this results in faster access since there are fewer hops. And for the ISPs, it's more economical because they don't need to pay fees to a third-party Network Service Provider (NSP).
Peering can also involve more than two ISPs, in which case all traffic destined for any of the ISPs is first routed to a central exchange, called a peering point, and then forwarded to the final destination. This is similar to the Network Access Points (NAPs) managed by the NSPs, but on a smaller scale.