Don't most devices lose time if there's no power? You can attach a battery to the arduino in case it loses power. It handy so you don't have to reset all of the settings.
Yes, most devices will lose time if there is no power. The battery does not go directly to the Arduino per se, instead, the DS1307 RTC has space for a 2032 button battery, so it will be able to keep track of time even in case there is a power loss.
The 5V line in is so that the Arduino can query the IC for the correct date/time. Then you can throw it all onto an LCD (or have the microcontroller query the RTC if it requires that information, i.e. for a timer).