Many themes provide sidebars on one, either or both sides (left and right). You can use the search filters to locate them here http://wordpress.com/themes/
However, mobile and tablet use is exploding so what's new is responsive width themes. Responsive width means the layout adapts depending on the size of the device being used to view your site. When responsive width themes are viewed on mobiles sidebars appear below the posts in order to provide as much space as possible for reading. http://theme.wordpress.com/themes/features/responsive-width/
That means you ought to disable the mobile theme which you cannot edit here > Appearance > Mobile because the theme is a responsive width theme.