What is a scintillation counter? Why would anyone need one? What can it do? 

A scintillation detector is a type of radiation detector that relies on a characteristic of various materials called Scintillation. This is the ability of a material to convert high energy photons (such as X-rays or Gamma rays) to lower energy photons (usually blue light) with a direct correlation between the number of photons emitted and the energy of the incident X-ray or Gamma ray. This relationship between incident energy and output "brightness" of a scintillation event is critical for Gamma Spectroscopy.

The light emitted by the scintilator is then picked up by a photomultiplier tube. PMT's are very interesting vacuum tubes and I can't possibly explain them in enough details here. In short, PMT's take in light and output a current proportional to the incident luminous flux.

See where we're going? Energy to light output -> Light output to current -> current over a resistor to a voltage -> profit?

That's the basics.