If an LED has a voltage drop across it of say 3V, each LED will drop that input voltage by 3V if they are in series, so by the time you get to the last LED the voltage to plug into Ohms law has significantly dropped, so your 100R resistor will sufficiently limit the current to allow <=20mA to flow through the LEDs.
If you put the LEDs in parallel, with the 100R resistor, you will suddenly get around 200mA through the LEDs, in turn blowing the arse off them.
Which is why, when you see some circuits for Christmas trees or Valentines hearts they use a certain number of LED's, a 9V battery and no resistor, this is because the voltage drop (also called Forward Voltage, Vf) is significant enough to not require one, things like batteries have internal resistance, so bear this in mind also.