You can also or right click on a heading or a selection of cells and choose Delete from the shortcut menu.
Clearing, as opposed to deleting, does not alter the structure of the worksheet or shift un-cleared data cells. When you want to clear a cell or range of cells, choose Clear from the Editing group in the Home tab.
What can be confusing about this process is that you can use the Delete key to clear cells, but it does not remove them from the worksheet as you might expect.