Great questions!
As to why Earth is layered, early in its history it got hot enough (from gravitational compression, the energy of impacting bodies, and radiation, to have partially melted. When this happened, the densest material sank toward Earth's center, while the less dense stuff rose to the top. It's a little like a hot chocolate-- foam floats to the surface, and the heavy syrup settles to the bottom.

The major layers of the Earth, starting from its center, are the inner core, the outer core, the mantle, and the crust. These layers formed as the building blocks of Earth, known as planetesimals, collided and collapsed under their own gravity around 4.5 billion years ago. At that time, the heaviest elements (like iron and nickel) sank to the core, while the lighter elements (like silicon, oxygen, and carbon), rose to form the mantle and crust.

The crust itself is composed of many layers, which are the ones we can see at the surface. Most continents have a crystalline core, known as a 'kraton'. Every continental kraton is then draped in many layers of sedimentary, igneous, and metamorphic rock. The most dramatic layers, like those in the mountain ranges above Santa Barbara, are often sedimentary rocks, which formed as long-gone mountain ranges eroded away and the resulting sediments were deposited somewhere else on the continent. A change in tectonic plate motion then caused those sedimentary layers to be brought up to where we can see them today.

When volcanoes erupt, the lava that comes out can spread across broad areas, forming a layer of igneous rock within the sedimentary layers. Thus, most of the layering on the Earth's surface is due to erosion and deposition of mountain ranges, and lava flowing out on the surface.

Layers of rocks are formed when sediment is laid down, and flattens out to be as close to the center of the Earth as possible. Then, a new layer is laid down, which has to fall onto the older layer, and thus lies above it.