What's up with the "jelly sandwich" analogy of the lithosphere, asthenosphere and mesosphere?
The introduction to Morgan et al., 2013 has a good summary of the features you are asking about, as well as proposing a mechanism for why it happens. 

From the intro:


  The Earth’s mantle underneath the tectonic plates, commonly referred
  to as asthenosphere, is known to be the lowest viscosity region of the
  upper mantle. Several potential mechanisms have been suggested to be
  responsible for this low viscosity zone. These mechanisms...include:
  (1) the temperature and pressure dependence of the mantle rheology may
  lead to a viscosity minimum between 70 and 200 km depth; (2) a small
  and immobile fraction of partial melts may weaken the mantle; (3) wet
  mantle below its dry solidus (deeper than about 70 km) would be
  expected to be weaker than shallower mantle that dehydrated during
  partial melting at mid-ocean ridges (MOR)—but this mechanism does not
  explain the physical origin for the base of the asthenosphere; (4) a
  reduction in mantle grain size within the asthenosphere.


The paper's proposed cause for this is that: 


  the sub-oceanic asthenosphere forms because it is the ‘graveyard’ for
  rising (i.e. hotter-than-average mantle) plumes. In this view, below
  the plate-age-dependent 60–100 km-thick oceanic lithosphere there
  exists a pool of hot plume material that has risen as far as the
  overlying thermal and/or compositional lithosphere  will allow.


Whether that mechanism is correct or not, only time will tell. In conclusion, due to the temperature and pressure characteristics of the asthenosphere, it is less viscous than the chemically identical mesosphere. This may be because of its place on temperature and pressure curves, because it contains pockets of partially molten rock, because rising mantle plumes make the asthenosphere actually hotter than the mesosphere, or otherwise.