In dynamic routing, routing tables are created dynamically by obtaining the network information from other routers. Routers in the network must be constantly updated to changes in the network topology. Routes may be added or removed, or routes may fail due to a break in the physical link.
When a new link is added or a link fails or changes, updates are sent by routers across the network that describe changes in the network topology. Other routers in the network then runs a routing algorithm to recalculate routes and build new routing tables based on the update information.
After recalculation, all the routing tables have arrived at a common view of the network topology. A converged network topology view means all the routers agree on which links are up, which links are down, which links are running fastest etc.
Convergence time is the time which a group of routers reach the state of convergence. Optimally the routing protocols must have fast convergence time.