Any photo or image you create in FotoFinish can be saved with transparency, but it is typically useful only when you have isolated a selection that you want to float over another image or a web page. The selection may be an object, person, piece of type, or anything that can be isolated from an image.
One way to isolate an object is to select it in the original photo, then copy and paste it into a new image window. In the new window it will be surrounded by the Background Color.
A selection is isolated from a photo
The selection pasted into a new window
Remember, the background color which matters for transparency is not necessarily the visible background color of the image, but the Background Color specified in the Tool Settings Panel.
To save the image with transparency, you can simply choose Save As from the file menu and select the GIF or PNG file format.