When you are lying down your lymph glands are better able to filter the fluids in your body, especially the fluids you are retaining. Have you ever noticed that when you lie down you have to get up and go to the washroom within 20 minutes or so when you go to bed at night?
Also, lying in a horizontal position, allows for better circulation in your body, because your feet are approximately the same level as your heart. This too makes it easier on your body to eliminate excess fluid you might be retaining. All this excess fluid makes us look and feel fatter during the day.
Lastly, when we sleep at night we are "fasting" in that we do not eat food until we get up in the morning. So when we wake up,our stomachs are empty (as monisajda mentioned) making our tummies look flat.