What many people don’t know: Gnome has a built-in screen recorder.
Press Control+Shift+Alt+R to start a recording of the desktop. A red light will appear in the lower right corner to show you the screen is currently being captured. Press the same key combination again to stop the recording. The video will be saved automatically in your home directory in WebM format.
In Ubuntu there is additionally a very nice software with more options included: Kazam