A routing protocol such as OSPF which permits routers to exchange information with one another about the reachability of other networks and the cost or metric to reach the other networks.
The cost/metric is based on number of hops, link speeds, traffic congestion, and other factors as determined by the network designer. Link state routers use Dijkstra's algorithm to calculate shortest (lowest cost) paths, and normally update other routers with whom they are connected only when their own routing tables change.
Link state routing is an improvement over distance-vector routing protocols such as RIP which normally use only a single metric (such as hop count) and which exchange all of their table information with all other routers on a regular schedule. Link state routing normally requires more processing but less transmission overhead.