There are two drawing modes used to select and unselect cells of the grid:
When the 'Draw with pencil' button of the toolbar is selected, the cursor will act like a pencil on the grid. By holding the left mouse button and dragging across the grid, the cells that the cursor passes over will become selected if not already selected. By holding the right mouse button and dragging, any cells that are already selected will be unselected (or erased).
When the 'Select rectangular region' button of the toolbar is selected, the cursor will provide the ability to select rectangular regions of the grid. By clicking and holding the left mouse button then dragging the mouse to form the desired rectangle, the cells within the rectangle can become selected by simply releasing the left mouse button. Conversely, in order to 'erase' cells that are selected within a rectangular region, do the same but holding the right mouse button instead.
In either drawing mode, by clicking and/or holding the left mouse button cells of the grid can be selected, which means they will then become black. Alternatively, by clicking and/or holding the right mouse button cells of the grid that are currently selected can be unselected, or erased, turning them back to their original color.