Domain mapping allows you to use your own domain instead of the [you].slideshowpro.com subdomain you're currently using. Domain mapping is a paid upgrade, and can be purchased through the Preferences link at the top-right of SlideShowPro Director's interface.
You will need to add a CNAME for the domain you wish to use at your DNS provider. Most DNS providers provide a utility where you can edit your DNS zone and add a new record. In doing so, you would enter the domain you wish to use as the Name, set "CNAME" as the Type, and your slideshowpro.com subdomain (eg, you.slideshowpro.com) as the Value. Every DNS provider is different, so check your web host's documentation for more information on setting up CNAMEs if necessary.
Technically, yes. If you have a domain that is not being used for anything online, you could use the whole domain (eg, "mydomain.com"). But if you already have content there and want it to remain accessible, you should setup a subdomain (eg, "photos.mydomain.com") and then modify the CNAME Type for that to point at your slideshowpro.com subdomain.