the resistor limits the current going through the LED and the current needs a path from the plus and minus/gnd to flow through. You can put your resistor on either side of the LED. For 5 volts a 220 ohm resistor is common but go up to 12 volts you need bigger resistor. I max = 5v/220 ohm =22.7 mA without the LED. As long as your current is less than the safe max for the LED nothing burns. Also we don't want to exceed the Arduino max current output see page 30. And get a multimeter .