This is not what we walk on. The layers of dirt and silt that cover the crust are normally considered to be separate from it. The crust comprises the continents and ocean basins. It has a variable thickness, anywhere from 35-70 km thick in the continents and 5-10 km thick in the ocean basins. The crust is composed mainly of alumino-silicates. More info here.
Just under the crust is the mantle. It is composed mainly of ferro-magnesium silicates. It is about 2900 km thick, and is separated into the upper and lower mantle. This is where most of the internal heat of the Earth is located. Large convective cells in the mantle circulate heat and may drive plate tectonic processes. More info here.
Outer and Inner Core
There are two very distinct parts of the core: the outer and the inner core. The outer core is 2300 km thick and the inner core is 1200 km thick. The outer core is composed mainly of a nickel-iron alloy, while the inner core is almost entirely composed of iron. The outer core contains as much as 10% lighter elements than iron alloy. The inner core is thought to rotate at a different speed than the rest of the Earth and this is thought to contribute to the presence of the Earth’s magnetic field. More info here and even more here.