The experiment showed that energy emitted from the single quantum dot was not continuous, but in bunches, as the theory of quantum mechanics dictates. The down time between emissions is accounted for by the charge carrier moving to a lower energy state and then absorbing more energy to move to the higher state before being able to emit another photon.
Enclosing a small amount of a semiconducting material within another semiconducting material makes quantum dots. Additional energy in the form of light particles or photons causes a particle in the contained material to move to a higher energy state. In quantum dots the band gap of containing materials is higher than the band gap of the contained materials. That difference in band gaps leads to input energy being trapped in the smaller band-gap material. That energy is released in the form of a photon.