PGLS (Phylogenetic generalized least squares) is a method for testing for correlations of two continuously distributed characters that vary across species. For example, one might be interested in the correlation between body size (X) and metabolic rate (Y).

The phylogenetic tree is used to account for the fact that species are not independent data points. In this case, the tree is used to explain correlations in the residuals from the regression line of Y against X.

In this app, you can model the residuals under three models: Brownian motion (BM), a random-walk model common for comparative methods; Ornstein-Uhlenbeck (OU), a model where divergence is constrained away from some optimal value, in this case the regression line itself; and Pagel's lambda, a model that rescales the tree to effectively change the rate of divergence through time.

When you carry out this analysis, you are assuming that both the species values and the tree are known without error, that the relationship between X and Y can be described with a straight line, and that the model you select is reasonable as a description of how residuals from that line change through time.