Geologists hypothesize that the Earth's center is composed of predominantly iron. The outer portion of the center, known as the "outer core", is thought to be liquid iron. While the interior portion of the center, known as the "inner core" is thought to be solid iron.

This hypothesis is based upon two important observations. First, energy waves known as "shear waves" do not travel through the outer core. Secondly the Earth has a magnetic field.

A Geologist uses seismometers to measure shear waves caused by earthquakes. Once shear waves hit the outer core the wave 'disappears' and once it hits the inner core it reappears. Think of a shearing force as the force needed to rub your hands together. This sliding or shearing force cannot travel through liquids because liquids do not resist shear waves. Shear waves do travel through solids however. Therefore since we see shear waves disappear at the outer core and reappear at the inner core geologists hypothesize that the outer core is liquid and the inner core is solid.

Regarding the Earth's magnetic field, the Earth exhibits a magnetic field that reaches above our atmosphere. For a magnetic field to exist, either a permanent magnet must be in the Earth's interior, or ionized molecules are moving in a liquid medium in the Earth's interior. A permanent magnet cannot exist in the Earth's interior due to the high temperatures deep in the Earth. Therefore the magnetic field is thought to be produced by ionized iron moving about in the Earth's liquid outer core.

You pose an excellent question. The composition of Earth's interior is critical to all life on Earth. If Earth did not have a liquid outer core the Earth would not have its magnetic field. Earth's magnetic field protects us from cosmic and solar energy that would prevent life as we know it.

The main evidence for the structure of the Earth comes from studying waves generated during an earthquake. When stress builds up and rocks at depth break, then elastic waves, just like sound waves are sent from the point of rupture. These wavesspeed out and move through the earth. When we put seismometers on the surface of the Earth, these waves can be measured. In particular, if we have enough seismic stations and the quake is big enough, then we can take all the travel time information and invert it. That means we can obtain a graph that shows the density of rock as a function of depth. Once we know the density we can estimate what the actual materials are. We find that the earth has a small inner core made out of iron surrounded by a larger outer liquid iron core and THAT is surrounded by a rocky mantle and rocky crust.

If you want to know more about this, you should study seismology. A good place to START is

Good question!
Earthquakes (and nuclear tests) cause seismic waves that travel through the Earth's interior, but these waves travel at different speeds depending on what kind of material they are traveling through. By having listening posts scattered around the planet, we can deduce what layers the Earth's interior to possess based on how long it takes for these waves to reach the listening post from the earthquake that produced them. We then can match the speed of these seismic waves with materials we are familiar with and identify what the Earth's interior is made of - at least in theory.

We also know how dense the Earth is by how strong the Earth's gravity is, and we know that the Earth's average density is about 5 grams per cubic centimeter. Rocks have a density less than 3 grams per cubic centimeter, which means that much of the Earth's core must be made of denser stuff in order for the whole planet to average out to 5. Metals have a density around 10 grams per cubic centimeter, so we speculate that the Earth has a metal core. The speed of seismic waves through the Earth's very center, also suggest speeds similar to what you would get in very hot metal. So what is this metal? Well, based on how much of what kinds of metals there are in the solar system, we guess that it's mostly a mix of iron and nickel - but I don't think we actually know.

Scientists know about the Earths interior from observations of Earths gravity, seismic waves that travel through the Earth, and the Earths magnetic field, as well as from comparison with the chemical composition of meteorites and from experiments that simulate conditions at the center of the Earth. The first estimate of the density of the Earths core was made by Isaac Newton over 300 years ago. Because the strength of a planets gravitational field depends on its density, Newton was able to use his observations of the Earth gravity to calculate that the average density of the Earth was more than twice that of rocks at the surface. Thus, the interior of the Earth must be much denser than the rocks near the surface.

More detailed knowledge of the structure of the Earths interior comes from observations of seismic waves. When an earthquake happens, it releases energy that travels through the Earth in all directions as seismic waves. Two kinds of waves created by earthquakes are compressional (P) waves and shear (S) waves. Both of these waves can travel through solids, but S waves cannot travel through liquids. Scientists figured out that the outer core must be liquid because S waves do not pass through it, but P waves do. The behavior of P and S waves also indicates that the inner core is solid. The speed of seismic waves also depends on the density of the material through which they are traveling. Thus by observing many seismic waves from many earthquakes all over the world, scientists have been able to work out the density of different parts of the Earth (i.e. the core, mantle, and crust).

So, how do we know what the dense material at the Earths core actually is? Scientists believe that the overall chemical composition of the Earth is very similar to a kind of meteorite called chondrites, which formed at the same time the Earth was formed. We know a lot about the composition of the Earths crust and mantle, because we can observe those rocks that have been brought to the surface by geologic processes. By comparing the composition of rocks from the Earths crust and mantle to the composition of chondrites, we can see what elements are missing, and therefore must be found in the core. Theories about how Earths magnetic field is formed, as well as experiments done at high temperature and pressures give clues as to the actual composition of the Earths core. Based on all these theories and observations, scientists know that the Earths core is mostly iron with some nickel and lighter elements such as oxygen or sulfur.