Any color (gradient or solid) can be applied to an artboard's fill using the Color or Swatches panels or the Fill Tool. It will appear behind any objects placed on the artboard—therefore acting as a background color.
For information on applying colors to an artboard's fill or stroke, see the Selecting colors and Gradient editing topics.
The artboard's fill can also have a solid opacity or gradient transparency applied. This can be achieved using the Color panel or the Transparency Tool, respectively. For more information, see the Selecting colors 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.