They can measure reflectance or absorbance.
http://en.wikipedia.org/wiki/Spectrophotometer
Also..does a spectrophotometer measure concentration or absorbance?
http://en.wikipedia.org/wiki/Spectrophotometer
By scanning different wavelengths across the visible spectrum, the spectrophotometer can determine the absorption profile of the dye. This allows for the identification and quantification of the dye in the sample. In other words, each dye has its own unique absorption spectrum, and by using different wavelengths, the spectrophotometer can detect the absorbance of each dye at its specific absorbing wavelength.
Regarding your second question, a spectrophotometer measures both concentration and absorbance. Concentration refers to the amount or quantity of a substance in a given sample, which is often determined by measuring the absorbance of the sample at a specific wavelength. The relationship between concentration and absorbance is described by the Beer-Lambert Law, which states that absorbance is directly proportional to the concentration of the absorbing substance and the path length of the sample. By measuring the absorbance of the sample at a known concentration, you can then determine the unknown concentration of a substance using a standard curve or calibration curve.