X-ray binaries such as GRS-1915 feature a black hole and a regular star. The x-ray luminosity is likely related to the rate of mass flow into the black hole from the star so when there is a lot of mass flow the x-ray luminosity is high but this explanation seems to just beg the question as to why the mass flow would change over time.
Such objects are surrounded by an accretion disk, that is a disk of gas, the gas being accreted onto the central object. However, at this stage of its life, the accretion disk around the black hole of a binary system like GRS-1915+105 is strongly depleted. Therefore, the accretion rate is not sufficient to support a coutinuous burst. Matter fills the outer disk until a critical density is reached, that triggered an outburst. Mass from the companion star is lost by a Roche lobe overflow mechanism.