The Table List panel on the left of the Control Window is pretty straightforward - it lists all the tables currently known to TOPCAT. If a new table is introduced by loading it from the Load Window or as a result of some action such as table joining then its name and number will appear in this list. The currently selected table is highlighted - clicking on a different table name (or using the arrow keys if the list has keyboard focus) will change the selection. The properties of the selected table are displayed in the Current Table Properties panel to its right, and a number of the toolbar buttons and menu items refer to it.
If you double-click on a table in the list, or press Return while it is selected, that table's Data Window will appear.
Certain other applications (Treeview or even another instance of TOPCAT) can interoperate with TOPCAT using drag-and-drop, and for these the table list is a good place to drag/drop tables. For instance you can drag a table node off of the main panel of Treeview and drop it onto the table list of TOPCAT, and you will be able to use that table as if it had been loaded from disk. You can also paste the filename or URL of a table onto the table list, and it will be loaded.
Sometimes while a table is being loaded a greyed-out entry will appear in this list with text like "Loading SAMP table" or similar. Such entries cannot be selected, but they let you know that something is happening.