It's a configurable option in Klipper (which is the process that's handling the clipboard in this video). You can access klipper in your system tray and if you right click on it one of the options lets you open up the settings (it's also somewhere in system settings I think but I always just get there via the system tray icon).

You can also configure how many entries it'll remember, whether it should pop up at the mouse cursor position, and set up regular expressions to recognize certain types of text (e.g. URLs) to perform specific actions.