Spectrometers usage in science.

Spectrometers mean different things to different fields. Generally, it is an instrument used to disperse radiant energy or particles into a spectrum and measure properties such as wavelength, mass, energy, or index of refraction.

That said, physicists/chemists use a mass spectrometer to measure atomic mass. A mass spectrometer removes one or more electrons from an atom (this is the ionization phase). The spectrometer then sends the now net positively charged atom through a magnetic field, which exerts a force on electrically charged particles. Because of the missing electrons, the atom has more protons than electrons and hence a net positive charge. The magnetic field bends the path of the positively charged atom as it moves through the field (the deflection phase). The amount of bending depends on the atom’s mass. Lighter atoms will be affected more strongly than heavier atoms. By measuring how much the atom’s path curves, a scientist can determine the atom’s mass (detection phase)

In biological setting, this is used to detect the weight of biological molecules, such as proteins, quantify the density of samples containing a combination of unknown molecules, or the purity of a sample. I've personally only used this technique once in my life, when we isolated salicylic acid, and wanted to determine its purity: we calculated it purity at 47%, which meant we didn't perform the isolation process effectively

No I mean determining the wavelengths present from a light source. What labs can do that?

I remember using a spectrophotometer in my early years also. We used it to determine the amount of light transmittance a solution allowed when concentrated light passed through it. However, this isn't quite what you're asking. You simply want to know the wavelength of any light light source. In that case, you'd simply shine the light into the spectrophotometer directly. I'm not certain how it works, but according to Wikipedia, it uses a diffraction grating or a prism that causes the different wavelengths of light to bend at slightly different angles, which are then detected by some lens.