Dendrograms are a convenient way of depicting pair-wise dissimilarity between objects, commonly associated with the topic of cluster analysis. This is a complex subject that is best left to experts and textbooks, so I won't even attempt to cover it here. I have been frequently using dendrograms as part of my investigations into dissimilarity computed between soil profiles. Unfortunately the interpretation of dendrograms is not very intuitive, especially when the source data are complex (e.g. multivariate).
An example is presented below that illustrates the relationship between dendrogram and dissimilarity as evaluated between objects with 2 variables. Essentially, the level at which branches merge (relative to the "root" of the tree) is related to their similarity. In the example below it is clear that (in terms of clay and rock fragment content) soils 4 and 5 are more similar to each other than to soil 2. In addition, soils 1 and 3 are more similar to each other than soils 4 and 5 are to soil 2. Recall that in this case pair-wise dissimilarity is based on the Euclidean distance between soils in terms of their clay content and rock fragment content. Therefore proximity in the scatter plot of frock frags vs. clay is directly related to our simple evaluation of "dissimilarity". Inline-comments in the code below elaborate further.