In the case of headshots retouching means getting rid of any temporary imperfections in an image. The most obvious example is spots but it could be anything that is unlikely to be there when you walk into an audition at a later date.
Retouching is recommended because these temporary imperfections are distracting, eg a big spot on the end of your nose. By erasing them you simply have a cleaner image which is visually more pleasing and easier for Casting Directors to digest. Stray hairs are often retouched out for this reason. If you look particularly tired on the day then a bit of help around the eyes may be needed too.
What retouching is not is changing any of your permanent features. It should absolutely look like you but you on a very good day.