The Session save option allows you to save much of the information about the loaded tables in your current TOPCAT session. Unlike the Current Table or Multiple Tables options, the whole of each loaded table, along with other information about your use of it, is saved, rather than just the Apparent Table. The saved items include:
The list of loaded tables is shown, with a column of checkboxes on the left. By default these are selected, but you can select or unselect them by clicking. When the save is performed, only those tables with the checkbox selected will be saved.
The tables are saved as a multi-table fits-plus (recommended) or VOTable file. This is a normal multi-table file in that any FITS or VOTable reader can read the tables it contains, but it contains some specialised metadata encoding information of special significance to TOPCAT, marking it as a saved session. The upshot is that if you save a file in this way and then load it back into TOPCAT, the tables it loads will appear in very much the same state as when you saved them, in terms of defined and current subsets, row order, visible and invisible columns, and so on. If you process it with some application other than TOPCAT, it will look quite like the table you saved, but with some additional data and metadata.
Note however that the reloaded state is not identical to that before saving. One important difference is that columns and row subsets which were defined algebraically are saved and restored as fixed values, so it is no longer possible to edit the expressions. Another is that only state belonging to tables is saved, so that for instance plots will not be restored. Table activation actions are not saved either. It is possible that some of this may be changed in future releases.