Two things you can select in a Word 2016 table are the text inside the cells or the cells themselves. You can also select rows, columns, or the entire table. Here are some suggestions:
Triple-click in a cell to select all text in that cell.
Select a single cell by positioning the mouse pointer in the cell's lower-left corner. The pointer changes to a northeastward-pointing arrow, as shown here. Click to select the cell, which includes the cell's text but primarily the cell itself.
Move the mouse pointer into the left margin and click to select a row of cells.
Move the mouse pointer above a column, and click to select that column. When the pointer is in the sweet spot, it changes to a downward-pointing arrow (shown here).
Clicking the table's handle selects the entire table. The handle is visible whenever the mouse points at the table or when the insertion pointer is placed inside the table.
If you have trouble selecting any part of a cell, click the Table Tools Layout tab. In the Table group, the Select button's menu provides commands to select the entire table, a row, a column, or a single cell.