looking closer at script on your slideshow it is extremely basic... it works to transition images as designed but doesn't do anything more
More advanced scripts provide callbacks for various events that allow you to add extra code to make things you want happen
A simple example is changing a slide counter when slide changes
One of the most widely used jQuery slideshow plugins is cycle. It offers developer access to the internal events most notably an event before image changes and another after image changes, among many other user definable options
If you were to implement cycle you would create extra containers for your caption images and add animation code on the before event callback to slide out the visible caption, and on the after event callback ( when new image visible) animate in a new caption image
Here's a very basic demo but should be enough to get you started