The irradiation (or power) history refers to the specific power or energy released per unit time experienced by the fuel assembly.  The irradiation history includes all irradiation cycles within a reactor as well as the shutdown time between irradiation cycles.  The fuel assembly burnup is essentially the integral of the assembly irradiation history, neglecting the shutdown time.  Irradiation history may vary for different fuel assemblies within the same reactor core, since the specific power is different at different assembly locations within the core. Fuel assemblies are also generally rotated through several different reactor positions within the core over several irradiation cycles.  The differences in core location, cycles, and shutdown lengths result in fairly unique spent fuel assembly irradiation histories even though final burnup may be the same.