Convergence is the state of a set of routers that have the same topological information about the internetwork in which they operate.
[1] Convergence is an important notion for a set of routers that engage in dynamic routing.
All interior gateway protocols rely on convergence to function properly.
The Exterior Gateway Routing Protocol BGP typically never converges because the Internet is too big for changes to be communicated fast enough.
When a routing protocol process is enabled, every participating router will attempt to exchange information about the topology of the network.