For example let us take households with the yearly earnings in USD dollars 40k, 55k, 70k, 100k, 115k, 130k, 135k. Then if we require to cluster the households into the two clusters taking their earnings as a measure of similarity, then the first cluster would have the households earning 40k, 55k, 70k; the second cluster would have the households earning 100k, 115k, 130k, 135k.
This is because 40k and 135k are furthest away from each other, and we require to have two clusters, so they have to be in the different clusters. 55K is closer to 40k than to 135k, so 40k and 55k will be in the same cluster. Similarly, 130k and 135k will be in the same cluster. 70K is closer to 40k and 55k than to 130k and 135k, so 70k should be in the cluster with 40k and 55k. 115K is closer to 130k and 135k than to the first cluster with 40k, 55k and 70k...