ah, you installed it in your home dir, that is part of RAM, which means it should dissapear when you reboot.
yes it is all in CD or ram unles YOU tell knoppix to mount a partition, most likely you get everything in a "ramdisk" with a size depending on your available RAM...
there some things that require Dynamical things can happen, like temporarioly saving downloaded files...
and ofcource you can certainly install some things in your homedir if the dependencies are met...
firefox is one program that should work well to install in /home/knoppix, actually most programs if you know how and have a large enough ramdisk (some simple ones should ble realplayer10 and azureus).

are you sure you did not tell knoppix to do a permanent home or such?