X-ray fluorescence (XRF) is the emission of characteristic "secondary" X-rays from a material that has been excited by bombarding with high-energy photons.
When an atom is irradiated by electromagnetic radiation having energy high enough, it absorbs an incident photon and expels an electron from the more internal shells (Photoelectron).
The rearrangement of the remaining electrons between the levels of the atom involves the emission of a photon X whose energy is characteristic of the emitter atom. The physical phenomenon of fluorescence X is widely used by modern spectrometers for elemental an chemical determination on materials like metals, ceramics, glasses etc.
For quantitative analysis, what is used is the so-called "fundamental parameter method", a numerical calculation algorithm that, from the theoretical knowledge of the fluorescence process, allows to obtain quantitative data on sample composition.