When you start the Moovly Editor and create a new Moov, the background color of your Moov is white by default. You can change this default Stage color in the Stage Properties that you see on the right side of the Editor:
Click the white square to change the Stage color and a color picker will appear. Select a new color and just click in an empty area to close the color picker.
If you want a specific background color for a part of your Moov or Clip, you could use the square shape from the Infographics Library and put it to the back of all other Moovs (drag it to the lowest layer in the Timeline). You can also use a background image from VideoBlocks.