When you feed a LED a voltage over its forward voltage it will attempt to consume an unlimited amount of current. The resistor is there to limit that current to prevent the LED (or the Arduino pin!) from burning out. FWIW, typical 5mm LEDs will have a forward voltage around 2V and 20ma of current.
http://www.kpsec.freeuk.com/components/led.htmWith respect to the circuit diagram, you are correct; the 5V feeder to the breadboard is not required.