X-Ray Fluorescence

The energy of the radiation causes electrons in the material to excite: they jump to a higher energy level. Since the excited state is not a stable state, after a while the electrons will fall back to a lower level and emit radiation with a wavelength proportional to the difference in the energy between the higher and the lower energy level.
The electrons do not necessarily immediately fall back to their original level, it's also possible that this happens in several steps. Each step causes radiation of a different wavelength to occur.

Since the energy levels of electrons are different for different atoms, x-ray fluorescence can be used to determine the composition of a material. X-rays are made to fall on the material and the wavelengths of the radiation that come back are measured. Each kind of atom has its own spectrum, so the different atoms in the material can be recognized, and by comparing the intensities of the spectra the amount present of each component can also be determined.

Basically what you have is a machine that records the amount of secondary emmissions, or "bounce off," of X-Rays from a substance that is bombarded with gamma radiation (which are also x-rays).

The amount of x-rays that the dectector records can tell the observer about the element content of the material. This is where the intensity of the x-ray gun comes into play. With different wavelengths, you can detect the amount of different elements by the amount of flourescence, or the concentration of x-rays bouncing back.

It is a form of Spectroscopy, because the detector reads into a computer that displays the data in a spectrographic fashion - because the intensity of the flourescence will be spread out along a range of various wavelengths, usually with big spikes that tell you about the elemental and chemical content of your sample.

In Industry, this technique is very useful in determining the purity of a substance that is being sold or used to make products, like a chemical or an alloy.

In the sciences, it has a wide variety of uses. Geologists can determine mineral content of samples, Bioarchaeologists have used the method to determine the dietary habits of previous cultures via XRF analysis of bones.

Anyway, the basic principle is fairly easy to understand, but how it is actually applied can get fairly complicated depending on what you are trying to do. Your XRF set-up might include monochromators and crystals. These sorts of things are done to make sure the geometry of the x-ray streams are right and your detector is picking up only flourescence, and to help get the maximum efficiency out of your set up.