In a few words, a spectral fingerprint (also referred to as "spectral signature" in remote sensing) is a specific (in theory unique) configuration of the reflectance spectra which allows you to recognize a type of material or combination of materials. The reflectance spectra is the ensamble of the various reflectances of a given surface across all detectable wavelengths (also depending on spectral resolution of your sensor).

You can find some definitions and examples here:

http://www.esa.int/SPECIALS/Eduspace_EN/SEMPNQ3Z2OF_0.html

http://geog.hkbu.edu.hk/geog3610/lect-06.pdf

Pure elements, homogeneous materials and single minerals have usually a very typical spectral signature whilst mixed materials give you an averaged mixed spectrum so that you will need unmixing techniques to trace back the pure components.

See e.g.: ftp://ftp.math.ucla.edu/pub/camreport/cam09-30.pdf

In plain words, it means the relationship between the identity of different objects in the ground and their representation in the image. In other words, the brightness values in the image matrix are related to very specific features in the ground and this relationship can be characterized by measurement.

I totally agree with Mr.Filippo, take a look on the article below

You are identifying atoms, ions, and molecules by their patterns of bright emissions and dark absorptions.

I think its simply a signature of any individual class.