When you start Moovly and create a new project, your background color 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 square to change the Stage color and a color panel will appear. Select a new color and just click in an empty area to close the color panel.
If you want a specific background color for a part of your content or per Clip, you could use the square shape from the Infographics Library, give it the color you like, make it larger to fill the whole Stage and put it to the back of all other objects (rightclick and send to back in clip):
The Extended Library View will open. There you can enter a search term, for example "background" and filter for either images or videos:
Once you have inserted a background in your project, put it behind all your other objects, so that it doesn't hide anything. This background will be visible for as long as you make it in the Timeline. So if you want to use this image or video for the whole length of your content, make sure it starts at the first second and drag its right edge to the last second of your project: