When networks communicate routes using BGP, individual networks are identified using an Autonomous System (AS) Number as defined in RFC 1930. Each route communicated using BGP contains an AS path, an ordered list of ASes that the route has been advertised by.
As an example suppose that there are three networks, imaginatively named Network A, B and C, as per figure 1. These Networks have the AS numbers 64600, 64601 and 64602 respectively. Networks A and C are each directly connected to B. A border router is a router on the edge of a network that communicates directly with routers on other networks. BGP peering sessions are run between border routers in Networks A and B and Networks B and C. There is no direct link between Networks A and C, rather these networks see routes to each other that transit through Network B. This given, the AS path on a router in Network A for a prefix advertised by Network C would be 64601 64602, showing that the route originated from AS64602 and was transited through AS64601. In other words, traffic will travel through Network B to get to its ultimate destination, Network C.