The lithosphere is the outermost sphere of the solid Earth, consisting of the crust and the upper part of the mantle. The lithosphere is largely important because it is the area that the biosphere (the living things on earth) inhabit and live upon.
If it weren't for the tectonic plates of the lithosphere there would be no change on Earth. Tectonic plates shift due to convection currents lower down in the mantle, and this can cause the formation of mountains, the eruption of volcanoes, and earthquakes. While this can be devastating in the short-run, long term benefits are the formation of new plant life, the creation of new habitats and encouraging adaptation.
It is also the source of almost all of our resources, and is rich in elements like iron, aluminium, calcium, copper and magnesium, which humans have used for tools and machinery for millennia.
When the biosphere interacts with the lithosphere, organic compounds can become buried in the crust, and dug up as oil, coal or natural gas that we can use for fuels.
In combination with the atmosphere and hydrosphere (water), it provides a stable source of nutrients for botanical life, which produce glucose that higher organisms use for sustenance.