To transfer your photos see: http://support.apple.com/kb/HT4083
Syncing with your mac allows you to transfer the contents of your camera roll to the mac, but there is no way to sync your album structure with the provided tools.
Your signature says " Mac OS X (10.5.8)", so you probably cannot use shared photo streams or journals. These would allow you to transfer your photos in a more organized way.
You may want to get an app for this, see King Penguin's post: