Cell spacing is the area around the cell itself. Click for an explanatory diagram

This is the space between cells. It's easiest to understand this by setting the table border to 1 and then increasing the spacing number.

The distance between cells within a table. A table with a cell spacing of 5 will push each cell 5 pixels away from each other.

the pixels that are added between the cells' exterior walls

The amount of space (in pixels) between adjacent table cells. You can specify cell spacing when you add a table to your page.

The amount of space between cells in a table. Cell spacing is the thickness, in pixels, of the walls of each cell.