"Why would I want to save any cookies?"

In most cases, you probably don't want to save them. There are some cases where the cookies are used for storing password information on certain sites, or storing shopping cart information, etc. This is a very handy feature of Complete Cleanup as you can select, view, and save the cookies you wish to keep. By saving a cookie, some sites will not require you to sign on again, or your shopping cart information will be there next time you sign on, etc..... which is the reason why you may want to save a cookie in certain situations. (You will have to be able to recognize which cookie to save by using the cookie viewer, or by recognizing the name of the cookie matching the site name).
Most of the information in the cookie will not mean anything to you, as this information is used by the website you visit, as it knows what this cookie data means. Currently only IE cookies can be saved.