When computing most multiple comparisons tests (not nonparametric or repeated measures one-way ANOVA), Prism assumes that all the data are sampled from populations with the same standard deviation, so the multiple comparison tests use a pooled standard deviation from all the groups.
Prism does not report this pooled standard deviation, but it is easy to calculate. Find the MSerror, also called MSresidual, and take its square root (MS stands for Mean Square, one of the columns in the ANOVA table).
For one-way ANOVA or two-way ANOVA with no repeated measures, there is only one MSerror (or MSresidual) in the ANOVA table. For two-way ANOVA with repeated measures, see this document for the details of which MS value is used.
The pooled standard deviation is expressed in the same units as the data.