Wikipedia
The -medoids algorithm is a clustering algorithm related to the -means algorithm and the medoidshift algorithm. Both the -means and -medoids algorithms are partitional (breaking the dataset up into groups) and both attempt to minimize the distance between points labeled to be in a cluster and a point designated as the center of that cluster. In contrast to the -means algorithm, -medoids chooses datapoints as centers ( medoids or exemplars) and works with an arbitrary metrics of distances between datapoints instead of l. This method was proposed in 1987 for the work with l norm and other distances.
-medoid is a classical partitioning technique of clustering that clusters the data set of objects into clusters known a priori. A useful tool for determining is the silhouette.
It is more robust to noise and outliers as compared to -means because it minimizes a sum of pairwise dissimilarities instead of a sum of squared Euclidean distances.
A medoid can be defined as the object of a cluster whose average dissimilarity to all the objects in the cluster is minimal. i.e. it is a most centrally located point in the cluster.