X-rays are high-energy photons. Thus, they are electromagnetic waves (like radio waves, visible light, ultraviolet light, etc.), but are very high-energy and thus have a small wavelength.
X-rays can be used for scattering experiments, because their wavelike nature causes interference from scattered radiation. Their small wavelength makes them ideal for probing small length-scales (atomic, molecular, and nano), while their high-energy allows them to penetrate through samples.