Here's a breakdown of the key discontinuities:

* Mohorovičić Discontinuity (Moho): This is the boundary between the Earth's crust and the upper mantle. It's marked by a sharp increase in seismic wave velocity, indicating a change in the rock composition and density.

* Gutenberg Discontinuity: This separates the Earth's mantle from the outer core. It's characterized by a sudden decrease in seismic wave velocity, indicating a transition from solid rock to liquid metal.

* Lehmann Discontinuity: This boundary separates the Earth's liquid outer core from the solid inner core. While seismic waves slow down at the Gutenberg discontinuity, they speed up again at the Lehmann discontinuity.

Other potential "breaking points":

* Lithosphere-Asthenosphere Boundary: This is a less distinct boundary, but it marks the transition from the rigid lithosphere (crust and upper mantle) to the more ductile asthenosphere (upper mantle). It's important for understanding plate tectonics.

* Inner Core Boundary: The boundary between the solid inner core and the liquid outer core.

Why these boundaries are important:

* Understanding Earth's structure: They reveal the distinct layers and compositions within our planet.

* Plate tectonics: The movement of tectonic plates is driven by convection currents in the mantle, which are influenced by these boundaries.

* Seismic wave propagation: The way seismic waves travel through the Earth is affected by these boundaries, allowing us to study the Earth's interior.

Note: "Breaking point" is a bit of an informal term. It's more accurate to use "discontinuity" or "boundary" when discussing these transitions within the Earth.