The share of light a surface sends back, measured wavelength by wavelength.
Spectral reflectance runs from 0 (absorbs everything) to 1 (returns everything) at each wavelength. A surface's colour under a given light follows from its reflectance multiplied by that light's spectrum.
Reflectance is a property of the surface; colour is what results when a particular light and a particular observer meet it.
A red paint has high reflectance above about 600 nm and low reflectance elsewhere.
Spectrophotometers measure reflectance because it is the one description of a surface that holds under every light.