Light
What is light? Well, it's what we see; but it's also much more than this. A few items that might help:
We describe light in terms of its wavelength. This describes its color (at least when light is visible), much in the same way that a wavelenght of sound describes a pitch.
How do we know that light is a wave in the first place? One reason is the fact that those diffraction gratings work in the first place. They rely on the diffraction of light, and diffraction only happens for waves.
Using the diffraction gratings and/or spectrascopes, we could see different wavelengths of light for different sources. For an incandescent bulb, we saw a full rainbow of colors, but the shortest wavelengths (blue and purple) would disapear whenever the temperature of the light source decreased. This relationship -- how shorter wavelengths become more prominent as temperature increases -- is known as Wien's Law. We could also see other spectra of other sources. Different gases produced emission spectra -- specific wavelengths were "on", but no continuous spectrum. Outside, looking through the Earth's atmosphere at stray sunlight, we saw an absorption spectrum in which the rainbow was mostly continuous, but with specific wavelengths missing.