An FBG is essentially a filter, and can act like a mirror for particular wavelengths. It is a piece of fiber treated with two interfering beams of ultraviolet light that form an interference pattern within the core of the fiber. The interference pattern allows particular wavelengths to reflect. FBGs are also used in dispersion compensation, and gain flattening.
A fiber Bragg grating is a type of distributed Bragg reflector constructed in a short segment of optical fiber that reflects particular wavelengths of light and transmits all others. This is achieved by adding a periodic variation to the refractive index of the fiber core. A fiber Bragg grating can therefore be used as an inline optical filter to block certain wavelengths, or as a wavelength-specific reflector.