Why An LED is a diode, so it only conducts when forward biased, meaning the anode is positive with respect to the cathode. As that forward current flows across the junction, electrons recombine with holes and release the energy as photons. No current, no light, so the LED's brightness tracks the forward current through it (which is why a series resistor is used to limit it).
Watch out Reverse current is what a diode blocks; applying reverse voltage gives only tiny leakage and, if you exceed the reverse breakdown rating, you damage the LED rather than light it.
LEDs are forward-thinking: current has to flow forward through the junction to make light.