A simple summary can be found at the wiki for explanations, but the lithosphere is the upper and solid part of the mantle.
http://en.wikipedia.org/wiki/Lithosphere
It is broken up into the tectonic plates. The depth is typically consider the limit of where this is still brittle material and not yet thick fluid. Understand it is not sudden transition, but it just keeps getting hotter until the rock is soft as you go deeper. About 1,800°F and the rock gets soft enough to consider the end of the lithosphere or the bottom of the plates.
The depth of this varies from 25 miles to ~175 miles deep. Ocean is typically thinner.
The Kola Superdeep Borehole is the deep drilling ever done, ~7.5 miles deep.
Thank you
Good study material
TT