I'm having a little trouble understanding as to what the voltage drop across an LED actually does in terms of the electrons. I understand that the potential difference across an LED causes the electrons to move and then undergo recombination to emit light, but why does it only happen significantly at a certain potential difference. What happens at lower potentials?
An LED is a diode. A diode is a semiconductor. At potentials lower than the forward biased voltage drop, very little current would be flowing. As the potential rises, more current is able to pass through (exponentially).
For more information, research semiconductor doping.