A spectrograph is a device that separates a signal into its component wavelengths. The easiest way to picture this is thinking about a prism splitting white light into colors.
In fact, a prism is a type of spectrograph. Specifically, prisms work through dispersion. With the wavelengths dispersed, they can be measured as a spectrum by the detector instead of as one beam. Most spectrographs don’t use prisms, however. They use diffraction gratings, which are more efficient.
Note: You might also hear the term “monochromator” when talking about spectroscopy experiments. A monochromator is the same as a spectrograph, except that it separates one wavelength at a time and typically has moving parts, i.e. it is monochromatic. All StellarNet spectrometers have spectrographs, not monochromators.