Nautilus left panel modification
Solution 1:
You can disable (or enable) the left sidebar entirely by pressing the F9 key.
If you are willing to hide only the text, but keep the icons, I don't think that's easily doable. Note that there aren't actually two columns (i.e. one for the icons and the other for the texts). There is a single column and the illusion of two columns is created by the theme Ubuntu uses. With the GNOME-default Adwaita theme it would look something like this: