To enhance a photo, it's pretty straightforward. Tap on the Enhance icon and let your iDevice do its magic. Once it is done, you will be presented with a picture that has had the color, shading, and overall appearance enhanced.
Sometimes enhancing a photo truly makes the photo look better, and other times the original still looks better. If you are happy with the new, enhanced photo, press Save; if not, press Cancel.
Once you are all done making changes to your photo, make sure to press Save. But be warned, currently there isn't a "save as new" option, meaning your edited picture will take the place of the original. Hopefully this is something Apple will add before iOS 5 is released to the public.