That space is controlled by two settings:
- A left paragraph indent, which is probably irrelevant here, since you probably haven't applied any indent.
- The cell margin. By default, this is 0.08" left and right (with the intent of allowing space between text and a border). You can change this for a given cell or for the entire table. For the most part you will want to change this for specific cells; if you reduced the left and right margins to 0" for the entire table, all the table text would run together. Right-click in the relevant cell and select Table Properties... In the Table Properties dialog, select the Cell tab and click Options.... There you'll see the margin settings for the selected cell. You'll need to clear the check box for "Same as the whole table" in order to change the settings for the given cell.