Accessory pigments within chloroplasts are responsible for

The answer is: to absorb photons of a different wavelength of light than chlorophyll.

Chlorophyll absorbs some wavelengths of light (~400-700 nm) and acts in photosynthesis. However, some other pigments, accessory pigments, can be found within chloroplasts. They have different absorption spectrum and thus can absorb photons of a different wavelength of light than chlorophyll. This is important if there is not enough light in the spectrum that chlorophyll can absorb so the photosynthesis can occur without a problem.