Live media often is a perfect showcase for an Operating system, Desktop Environment or any other thing you want to show. Also, since Live media is read-only, live media perfectly allows for a kiosk system, a system that may change while it's running, but restores all original settings when rebooted.

Live media is also installable. You start out with a system and boot it from live media, then choose to install the live media. This however is inferior to real installation media, but is convenient if you happen to like what you see when running from live media.