Beta diversity represents the explicit comparison of microbial communities (betweensamples) based on the measure of the distance or dissimilarity between each sample pair. Beta diversity is calculated for every pair of samples to generate a distance or dissimilarity matrix, and then apply ordination based methods such as Nonmetric Multidimensional Scaling (NMDS) or Principal Coordinates Analysis (PCoA) for visual representation at lowdimensional space (i.e. 2D3D scatter plots).
MicrobiomeAnalyst allows user to choose from various beta diversity metrics including

BrayCurtis dissimilarity is simply calculated as: 1(2w/(a+b))
where w is the sum of the of the lesser scores for only those species which are present in both communities, a is the sum of the measures of taxa in one community and b is the sum of the measures of taxa in the other community.  Jaccard index is computed as 2B /(1+B), where B is Bray–Curtis dissimilarity.
 Jensen–Shannon divergence (JSD) is a method of measuring the similarity between two probability distributions. It is also known as total divergence to the average. JSD is based on the Kullback–Leibler divergence. The square root of the JSD is a metric often referred to as Jensen–Shannon distance
 UniFrac distances are based on branches in a phylogenetic tree that are either shared or unique amongst samples. The unweighted UniFrac only consider the presence or absence of the species, while weighted UniFrac consider the actual abundance. The key feature of phylogenetic treebased distance is that differences in community structure attributable to closely related organisms are weighted less heavily than are differences arising from distantly related organisms. Please note, user must provide a phylogenetic tree (.tre, .nwk) to MicrobiomeAnalyst (in Data Upload step) in order to use UniFrac distances
Further details on different measures of diversity can be found here.