A dendrogram is a tree data structure that allows us to represent the entire clustering hierarchy produced by either an agglomerative or divisive algorithm. The idea is to put the samples on the x axis and the dissimilarity level on the y axis. Whenever two clusters are merged, the dendrogram shows a connection corresponding to the dissimilarity level at which it occurred. Hence, in an agglomerative scenario, a dendrogram always starts with all samples considered as clusters and moves upward (the direction is purely conventional) until a single cluster is defined.
For didactic purposes, it's preferable to show the dendrogram corresponding to a very small dataset, X, but all the concepts that we are going to discuss ...