Any colour (gradient or solid) can be applied to an artboard's fill using the Colour or Swatches panels or the Fill Tool. It will appear behind any objects placed on the artboard—therefore acting as a background colour.
For information on applying colours to an artboard's fill or stroke, see the Selecting colours and Gradient editing topics.
The artboard's fill can also have a solid opacity or gradient transparency applied. This can be achieved using the Colour panel or the Transparency Tool, respectively. For more information, see the Selecting colours and Transparency topics.
However, artboards also have an overall Opacity property which is controlled on the Layers panel. Adjusting the opacity of the artboard in this way will affect all objects placed on the artboard.