Clustering is part of the unsupervised family of statistical/machine learning tasks and is similar to classification, but a little bit more difficult since we do not know the correct labels!
If we do not know the correct labels we can try grouping data points together. Loosely speaking, points that are closer between themselves, under some metric, are defined as belonging to the same group and separated from the other groups. Clustering has many, many applications; for example, phylogenetics, a branch of biology studying the evolutionary relationships among biological entities, can be framed as clustering techniques applied to and guided by an evolutionary question. A more capitalist-driven application of clustering is determining which movie/book/song/you-name-the-product we may be interested in. We can try to guess this based on our consumption-record and how this record clusters with those of other users. As with other unsupervised learning tasks, we may be interested...