The maximum absorption in the UV-Vis spectrum of colloidal solutions is related to the average particle size, while the bandwidth is related to the dispersion of the particles. This information is possible due to the effects on surface plasmon resonances.
The above answer only applies to metallic particles which have a surface plasmon resonance, which is dependent on particle size. This is not the case for most nanoparticles, for which the spectrum depends on the chemistry of the material.