What geological mechanisms result in the great depth of the Mariana Trench?
As taken from Wikipedia:

There are several factors that control the depth of trenches. The most important control is the supply of sediment, which fills the trench so that there is no bathymetric expression. It is therefore not surprising that the deepest trenches (deeper than 8,000 m (26,000 ft)) are all nonaccretionary. In contrast, all trenches with growing accretionary prisms are shallower than 8,000 m (26,000 ft).
A second order control on trench depth is the age of the lithosphere at the time of subduction. Because oceanic lithosphere cools and thickens as it ages, it subsides. The older the seafloor, the deeper it lies and this determines a minimum depth from which seafloor begins its descent. This obvious correlation can be removed by looking at the relative depth, the difference between regional seafloor depth and maximum trench depth. Relative depth may be controlled by the age of the lithosphere at the trench, the convergence rate, and the dip of the subducted slab at intermediate depths.
Finally, narrow slabs can sink and roll back more rapidly than broad plates, because it is easier for underlying asthenosphere to flow around the edges of the sinking plate. Such slabs may have steep dips at relatively shallow depths and so may be associated with unusually deep trenches, such as the Challenger Deep.


A simple picture for anyone who doesn't understand how these trenches form:

(source: wikispaces.com)
Also, the Mariana Trench isn't the only super deep trench in the ocean... 10 deepest parts of the ocean