Distance Vector type protocols work on the basis of distance vectors….or arrays of distances to known networks. Vector refers to a uni-dimensional array. Distance refers to the measure of feasibility, or a metric of reaching a particular network.
Messages between routers for distance vector protocols contain arrays, with each array element containing information about one particular network know to the originating router of the message as well as the distance to that same network.
Routers learn of these networks by hearing about them from other adjacent routers, the advertising router becomes the next hop to the learned network, and that information is passed along to other routers, this is how distance vector protocols learn of the network and distance metric to reach a network.
If multiple adjacent neighbors advertise the same network element, then the distance vector protocol will make a decision on which route is better based on the metric for the advertised route and inject that route into the routing table. Once this happens the router begins advertising it’s known routes to the networks it’s aware of to other devices.
Processing of exchanged routes is simple and not memory or cpu intensive, however its simplicity can be prone to create routing loops. There are a number of methods implemented into Distance Vector to avoid creating routing loops, however only EIGRP using it’s advanced properties is guaranteed to provide a loop free path in every instant.