Indeed, sometimes these great dust storms can become completely global. The storm is near the edge of the shrinking south polar cap. All dust storms require high surface winds to start and to be sustained. Also great dust storms, in particular, always occur close to southern summer on Mars which is the season when Mars is nearest to the sun and there is maximum solar heating. Several hypotheses have been advanced to explain the onset of regional and planet-wide dust storms but the sheer lack of data means that we cannot single out one theory in particular.
Higher winds lift more dust causing further amplification of the storm in positive feedback.
For a dust storm to extinguish itself and the dust to fall back to the surface, the winds must drop. Computer simulations show that as the atmospheric dust load increases, the vertical mixing of the dust decreases but winds near the surface continue to increase. This makes dust storm extinction difficult to explain. But maybe dust gets transported to regions where settling out is possible or perhaps the dust is scavenged by condensation of water vapor or carbon dioxide in the polar regions. Or if dust storms are caused by global resonance of the atmosphere then they would naturally extinguish themselves because a dusty atmosphere would no longer be conducive to resonance.