You may have noticed that when you clear all the tiles in the Afrika tileset, an attractive backdrop of Mt. Kilimanjaro appears. When you create your own tile sets, you can include a backdrop of your own as well. (See "Creating a Tile Set" for information on how to do that).
Once you have pasted in your tile set, a normally-dimmed menu item will become active, called "Paste Background Picture". This item will be active whenever there is no background picture associated with the current tile set.
As with creating tile sets, you draw the background picture in your paint program. The picture should be as close as possible to 512 x 320 pixels, but unlike the tileset picture, the background picture is not required to be exactly the correct size.
When you have drawn your background picture, select the whole picture with the marquee tool and choose "Copy" from the edit menu. Then exit your paint program and start up Mombasa. Choose the tile set that this background picture will go with, then choose "Paste Background Picture" from the Tile menu. That's all there is to it!