Back in 1913, little was known about the composition of the Earth's interior, so we'll excuse Webby's exclusion of this important topic.
When viewed in cross-section, the Earth is typically divided into three layers: the outer crust, the mantle and the core. British schoolchildren are given the analogy of a Scotch egg: with breadcrumbs (the crust), sausage (the mantle), the egg white (the outer core) and the yolk (the inner core). Of these three layers, the mantle is the most dynamic and perhaps the least understood.
The mantle is a thick layer of hot ultramafic rock. It is the source of much of the world's magma and is thought to be the driving force behind plate tectonics.
At its closest point to the Earth's surface, underneath oceanic crust near the mid-ocean ridges, the mantle starts at a depth of about 10 km. Underneath continental plates, this figure ranges from 30 km to 75 km. The mantle is thought to have a lower boundary at a depth of 2,890 km below the surface, where it interacts with the outer core.
It's possible to differentiate the mantle into several chemically-distinct layers. Firstly, the mantle is divided into an upper mantle and a lower mantle, which are separated by a transition zone. Even further breakdowns can follow:
Upper mantle (10-400 km) - The upper mantle is composed of solid ultramafic rocks, high in olivine and pyroxene content. The boundary of the upper mantle with the crust is marked by the Mohorovicic discontinuity or "Moho"; here seismic waves refract when passing across the boundary due to the differing compositions of the crust and mantle.
The upper part of this region interacts closely with the crust. Subducted crust is assimilated into the upper mantle, often at the expense of felsic minerals, which are fractionally melted and form volcanoes. In addition, mafic magmas generated in the lower mantle pass through the upper mantle on their way to the surface.
The topmost 50-120 km (depth varies regionally) of the upper mantle is considered part of the lithosphere, along with the crust. Below this lies the asthenosphere, a region where the mantle is partially-melted and behaves plastically. This plasticity acts as the lubricant for tectonic plates, which glide across the easily-deformed asthenosphere.
Mesosphere (400-660 km) - This is the transition zone between the upper and lower mantle. Here, the pressure from overlying rock is sufficient to overcome the temperature gradient, making the mesosphere rock stronger and less susceptible to deformation.
Chemically, the mesosphere is higher in calcium and aluminum. This region is thought to be the source of mafic (basaltic) magmas. Note: this is not the same mesosphere found in the atmosphere.
Lower mantle (660-2,890 km) - The lower mantle is separated from the transition zone by another seismic discontinuity, this one at 660 km. As with the Moho, this marks a compositional change between layers. It is thought that the lower mantle is richer in silica, iron and nickel.
At the base of the lower mantle is the D" layer, a poorly-understood layer marked by yet another discontinuity. This may be a iron-rich zone of transition between the outer core and mantle.
As mentioned above, the chemical composition of the mantle varies between its layers. Overall, the normalized composition of the mantle is estimated to be similar to that of the ultramafic rock peridotite (which is composed of olivine, clinopyroxene, orthopyroxene and chromite).
A synthesis of several estimates of the mantle's bulk composition follows (all figures in percentages):
SiO2: 46.4-48.1 MgO: 31.1-39.0
FeO: 7.6-12.7 Al2O3: 3.1-4.1
CaO: 2.3-3.3 Na2O: 0.3-1.1
Cr2O3: trace-0.6 MnO: trace-0.4
P2O5: trace-0.4 K2O: trace-0.1
TiO2: 0.1-0.2 NiO: trace-0.3
Just how petrologists are able to guess the chemical composition of rock lurking 2000 km below the surface of the Earth is interesting. A number of methods are employed, mostly using inductive reasoning. In some areas in the Alps and the Himalayas, some mantle rocks have been thrust to the surface (as part of ophiolite suites) and can be measured directly. Seismic analysis is important, as the seismic velocities for most materials and temperature-pressure conditions can be measured in labs. These are compared to seismic profiles to get a rough idea of the minerals present. Finally, some meteorites have been used to estimate the bulk chemical composition of the planet; once the iron and nickel has been subtracted from the composition of the meteorite (representing the Earth's core), to obtain a rough composition of the mantle.
The most common mantle minerals are olivine (Mg,Fe)2SiO4 , clinopyroxene (Ca,Na)(Mg,Fe,Al,Ti)(Si,Al)2O6 , orthopyroxene (Mg,Fe)2Si2O6 , garnet (Ca,Al,Mg)3(Al,Fe3+,Cr)2(SiO4)3 , chromite FeCr2O4 and perovskite CaTiO3. Mantle rocks are often found as xenoliths in kimberlites, and are reknown for playing host to diamonds.
After the return of Apollo 11, it was determined that the composition of rocks plucked from the Moon was roughly the same as the Earth's mantle, strengthening the hypothesis that the Moon formed from material blown off the Earth by a planetary collision.
As heat from the core and lower mantle escapes to the surface, it causes convection cells to form in the easily-deformed asthenosphere. These currents of partially-melted rock help quickly transfer this heat to the surface. It is this hot, moving material that keeps the Earth a dynamic planet. As hot mantle rock rises, it can fully melt into magmas, which then force their way through the lithosphere to form hot spots. These magma plumes may form volcanic chains (as in the Hawaiian Islands), and more importantly, are thought to drive the sea-floor spreading. This in turn is one of the driving mechanisms behind the movement of tectonic plates. The lateral movement of mantle rock at the topmost section of a convection cell also exerts a force called mantle drag on the bottom of a lithospheric plate, literally dragging it along the Earth's surface by its ass end.
Tectonics (1995), Moores & Twiss, W.H. Freeman & Co.
Moorland School, The structure of the Earth - http://www.moorlandschool.co.uk/earth/earths_structure.htm
Composition of the mantle - http://diotima.mpch-mainz.mpg.de/~jesnow/Ozeanboden/1997/Week3/Composition.html
"The viscosity structure of the mantle", Scott D. King, AGU - http://www.agu.org/revgeophys/king01/king01.html
"Earth's upper mantle", Sebastian Rost, Univ. of California Santa Cruz - http://www.es.ucsc.edu/~srost/diss_01/node5.html
"Shape, Size and Internal Structure of the Earth", St. Mary's University - http://www.stmarys.ca/academic/science/geology/earth/pubintro/shape.html