A spectroscope relies on separating light into its component parts because of the information that can be obtained from examining the wider spectrum of colors that composes white light as it is reflected off an object. Such information can include elemental composition as well as how much of a particular element makes up the object that is being looked at.
The process by which atoms retain photons of light is called absorption. When atoms in a material absorb certain wavelengths of light photons, these photons are not reflected from the object. The spectrum of light that is being reflected from an object that is shown by a spectroscope will normally have bands of black lines dispersed throughout it. These black lines show what wavelength, or color, of light is being absorbed by the object in question. By observing where these black lines fall on the color spectrum that is being perceived through the spectroscope, one can discern what elements make up the object or material.
This process is especially useful when investigating stars in our galaxy. By looking at a star through a spectroscope and analyzing the black bands that fall on the spectrum of light being emitted, scientists can accurately determine what elements the star is composed of.