The lithosphere is the brittle, outermost layer of the Earth & is made up of the crust (both oceanic & continental), as well as the upper-most bit of the mantle (we call that the mantle lithosphere). The lithosphere is distinguishable from the asthenosphere (below it), because it is a BRITTLE solid, whereas the asthenosphere (the majority of the mantle) is a DUCTILE solid - a moving solid that "flows" over VERY long timescales. Here's an example from NatGeo (source: https://www.nationalgeographic.org/encyclopedia/lithosphere/).

The lithosphere affects the ENTIRE Earth because it's the driving force behind plate tectonics - without plate tectonics, our planet would look a LOT different! At subduction zones see figure here (source: https://steemit.com/steemstem/@josue783/the-lithospheric-tectonic-plates), cold oceanic lithosphere is more dense than the overriding plate, so it sinks. As it sinks, the density of the plate increases (for a lot of complex reasons), and this actually PULLS the plate down into the mantle. The changes in temperature between the cold lithosphere and hot mantle help to drive convection currents within the mantle; these convection currents help to move the plates around too.