MOSFETs are voltage driven - their gate acts like a small capacitor so the charging/discharging of the gate causes current spikes. That's why you put a resistor between gate and Arduino pin.
When the Arduino starts up all pins are set to INPUT, so the gate of the MOSFET is floating. The MOSFET can be on, off, partly on... a pull-down resistor on the gate ensures it's guaranteed off.