If the phone isn't running in the background (and in Linux [which is the operating system that Android runs on], an app can be loaded and put to sleep, using no battery at all), when you get a phone call, Phone has to be loaded, which drains battery, takes time, and you may miss the call (since you won't hear a ring until Phone is fully loaded and running - waking it with a signal that says "the phone is ringing" takes microseconds).
Over 18 hours from 100% to 0% (what the graph is telling you) isn't bad. (Of course, you should never discharge a lithium battery lower than 40%, or charge it to more than "as soon as it shows 100%", which is probably between 95% and 98%. If the charger [the chip in the phone - what you plug into the wall is just a 5 Volt power supply] goes bad, it could keep charging a fully charged battery, heating it enough to boil all the electrolyte out of it - or even cause a fire or an explosion. Lithium batteries weren't chosen for safety, they were chosen for weight. [And if they could make batteries using helium or hydrogen, they would.])