What does it mean when a set of genes are positively correlated versus negatively correlated in the GSEA analysis? Does positively correlated mean those genes are upregulated in the sample?

That’s right. Positively and negatively correlated refers to whether a set of genes are enriched, or upregulated, in the group. If the pathway is positively correlated with the group, that means most of the genes of that pathway will also be positively correlated with the group.

Say you have a treated versus untreated group, and you see the table of results below.

Click on "Dox" to see the pathways that are positively correlated with the  treatment group, and "Control" to see the pathways positively correlated with the control group.