When you need to remove whole cells, rows or columns from a table, users rightly expect that when you select the cell(s), row(s) or column(s) and press Delete, they will be deleted. This does not happen, however. Instead, if the selection contains text, the text is deleted, but the structure remains intact. This is great if that’s what you want to do. However, if you really want to trim the structure, Delete doesn’t make it happen.
The simple but not-terribly-well-known solution is to use the Backspace key instead of the Delete key. When just cells are selected, Word will prompt for what you want to do.
If a whole row or column is selected, the Word will go ahead and delete it.
Of course, you can also right-click the selection and choose Delete Rows, Delete Columns, or Delete Cells… However, pressing the Backspace key—for me, anyway—is a lot more direct and satisfying. This works when the whole table is selected, too. Delete empties the table, while Backspace zaps it completely.