Unless there's something odd about it your camera should immediately appear as an icon on your desktop when you plug it in (i.e. mount like any external storage device), then you can access it via the Mac Finder exactly the same as via Windows Explorer (functionally, they're identical, just a file/folder manager that lets you access your drives; although the Finder does have a few extra features over Explorer, but that's not important right now); then you should be able to copy the files to your external HDD so you still have the originals backed-up there...