Sorry for the typo. The last four words should be "solid state lighting applications".
Quantum dots are usually semiconductor structures with spatial dimensions between of a few atoms to a few tens of atoms. Because of this small size, they exhibit physical properties situated somewhere between the atom itself and the entire crystal. For example while in an atom there will be only a few levels of allowed energy for the electrons, and in crystal an entire almost continuous band of allowed energies, in quantum dots there are a finite number of discrete energies that electrons can take. The smaller the dimension of the dots the smaller the number the allowed energies.
The applications of quantum dots in or day by day life are related to their high yield of generating light by electron-hole recombination or the high effectiveness of the reverse effect (generating electron-hole pairs when illuminated). This happens basically because the energy of excitons (excited electron-holes pairs = in other words difference between allowed electron levels) can be changed in a dot by changing its physical dimensions and thus fit the available external illumination conditions.
Therefore quantum dots are used to manufacture cheap solar cells at a cost much lower than 1 USD/Watt. Also quantum dots are used in manufacturing high efficiency luminescent displays and to cover the interior of illuminating lamps in solid state lightning applications.