Single-left-clicking on one of the table lines selects the whole table. The grips that show up now let you change the overall width and height of the table (expanding rows and columns equally), or to change the width of an individual column. The right-click menu contains the global table options, such as “size all rows equally”.
Single-left-click in an empty space or on text, though, and you get a whole new set of options. Now, just a single cell is selected. Grips here change only the height or width of the appropriate row or column, and the right-click menu contains cell-specific commands such as alignment and formatting.
If you left-click in an empty space, but hold down the button and drag, you can select a range of cells. The grips work the same as the overall table grips (rows and columns are resized equally), but the right-click menu is the same as for a single cell. However, if you select multiple cells, right-click, and pick “inserts rows/columns”, AutoCAD will insert multiples rows/columns – as many as you have selected.
(This tip applies mostly to 2007+; tables first appeared in 2006, but had very limited functionality.)