The earth formed by the accretion (or collision) of small protoplanets (objects that aren't large enough to be considered a planet) within the solar system.

When objects collide, they turn kinetic energy into heat. Therefore, the Earth was extremely hot as it formed, and the planet was molten.

Denser parts--like iron metal--sank to the center of the core due to gravity. Lighter parts--like lower density minerals that make up the crust--are buoyant and essentially 'float' on the top. This process is called differentiation. Today, our planet has an inner core made mostly or iron metal, a mantle composed of dense silicate minerals, and crust that is made of lighter silicates. These three chemical layers can be further broken down (for example, crust can be either continental or oceanic, with different chemical and physical properties), but in general this is a good way to think about the chemistry of the layers of the earth.

The layers of the earth can also be defined by their mechanical properties (rheology). An analogy is that both liquid water and ice have the same chemical formula (H₂O), but they behave very differently: ice is much more rigid. In a similar way, the layers of the earth behave very differently depending on their temperature and pressure.

When the layers of the earth are defined by their rheology, they consist of the lithosphere (=rock layer), which consists of the crust and the upper mantle, both of which behave in a rigid, brittle fashion. Below the lithosphere is the asthenosphere (or upper mantle), which is able to flow quite readily. Next is the lower mantle, which is generally more rigid than the upper mantle. The outer core is molten, and the inner core is at such high pressure that it is solid.

In summary, the layers of the earth formed by differentiation, or gravitational settling when the planet was molten. Once differentiated, the layers behave according to their mechanical properties, which are a product of chemistry, temperature, and pressure conditions.

We can slice up the earth into layers many ways based on different characteristics of those layers. Imagine a layered chocolate and vanilla cake with frosting on top. We could split the cake up into the "chocolate layer," the "vanilla layer," and the "frosting" layer based on what it's made out of, or you could split it into the gooey "frosting" layer and the springy "cake" layer based on what it feels like. There is one layer, the "frosting" layer, that is separate both of the ways we divide the cake.

Similarly to the cake, if we look at the earth some layers are different when you look at what layers are made out of or how they flow. If you look at the earth based on big changes in the types of minerals then we usually talk about three, sometimes four, layers: the crust, the mantle, the (inner and outer) core. When we look at how materials flow, which is similar to looking at how the cake felt, then we can say there are different layers, such as the lithosphere, which includes all of the crust and the top bit of the mantle, or the asthenosphere, which is the weak layer or mantle bellow the lithosphere on which tectonic plates move. Bellow the rest of the mantle there is the outer core, which is molten, and the inner core, which isn't. So there are many ways to look at the earth, but we choose whichever division we need depending on what we're interested in.

Iron is denser than rock. When the iron on Earth melted and sank to the interior shortly after the Earth first formed, the rocks floated on top. More recently, the core has begun to freeze, and molten iron is less dense than solid iron, so it sits on top of the solid inner core.

Lastly, the crust, because it is exposed to the air and ocean, gets colder than the plastic mantle beneath it, which is why there is a crust layer (it's also denser than the mantle below it, which is why we get subduction trenches in the ocean where ocean crust sinks into the mantle).