In biochemistry, we use devices which use the principle of surface plasmon resonance to study the binding between biological molecules. Even though I uses these machines, I'm still not to clear on how exactly they work. All I know that shining monochromatic, plane polarized light on a thin metal boundary between two materials with different indices of refraction generates a "evanescent wave" which will reduce the intensity of the totally internally reflected light at a specific angle, but I'm not exactly sure what the "evanescent wave" people talk about is nor why it reduces the intensity of the reflected light at a specific angle. Any clarification on these issues would be appreciated.

If it works in the way I am guessing just from reading your description, you want to read up on "bragg reflections" and crystal lattices...

If by Bragg relflections, you mean Bragg diffraction, I don't think that's relevant since SPR isn't used to calculate distances. SPR is used to measure the index of refraction of a layer of biological molecules, which is proportional to the mass of the molecules in that layer.