Jupiter's aurorae put on a permanent, ever-changing light show more than a thousand times brighter than the Earth's own aurorae. At ultraviolet wavelengths these aurorae are dominated by the ME: discontinuous ovals of curtain-like light partially encircling each of the planet's magnetic poles. The properties of these aurorae are a reflection of processes in Jupiter's magnetosphere, as the two are coupled together by currents flowing along magnetic field lines. By understanding auroral features in the ME, the vast Jovian magnetosphere's complex interactions with the planet can thus be better understood. The evolution of this energetic system has implications for Jupiter's present and past, as well as its place within the Solar System. While Jupiter's large-scale aurorae have been extensively studied, the properties, particularly motions, of small-scale auroral features represent a comparatively unexplored route to gain deeper understanding of this system. Here, the motions of these auroral features are characterized and related back to the physical processes in Jupiter's magnetosphere and ionosphere. First, a survey of auroral feature motions in Jupiter's ME is created based on Hubble Space Telescope observations. A dichotomy in auroral motion is found: features near dawn remain fixed in local time significantly more than features elsewhere. This finding gives context for Jupiter's dawn storms-- rare, enigmatic auroral phenomena noted for their fixedness, brightness, and appearance only at local dawn. Next, the ME is measured on smaller scales and compared with in-situ measurements of magnetospheric plasma flow from the Galileo spacecraft to estimate the magnetospheric and ionospheric properties associated with fixed auroral features. Finally, these properties are used to inform a self-consistent model of the currents generating the ME. Ionospheric conductance-- the ease with which currents flow through the ionosphere-- is varied to generate models which best match the auroral observations. Altogether, a coherent description of ME auroral features and their associated physical processes emerges. Increased conductance is found to correspond with both auroral emissions and the acceleration of magnetospheric plasma. The conductance, which is spatially variable but fixed in local time on average, is proposed to explain the motions of small-scale ultraviolet Jovian auroral forms.