This is a great question. The melting point of a solid depends on PRESSURE .

To give you an example from volcanology, to melt a block of now frozen basalt requires heating the rock up to about 1200 deg C (Centigrade) at the EARTH'S surface (pressure = 1 atmosphere). But if we buried this same rock under 30 km of rock, where the pressure is 10,000 atmospheres, we would have to heat the rock up to 1250 deg C to melt it.

The same is true of iron. The outer core of the Earth is liquid ... but as one dives deeper and deeper within the core the pressure increases. Finally a pressure is reached such that the ambient temperature is LESS than the freezing point...and so the iron liquid crystallizes to become a solid.

The melting point of MOST substances increases as pressure goes up. One notable exception is water.

From about 1 atmosphere pressure up to several hundred atmosphere pressure the melting point of ice actually DECREASES as pressure goes up!. This is very important to a hockey player! That is, when someone is on skates, the metal blade of the skate increases the pressure on the ice right beneath the blade. This LOWERS the melting point of the ice immediately beneath the blade and that makes some liquid water. This makes the ice SLIPPERY. Then as the blade passes by, the pressure is released and the film of water laying on top of the ice beneath where the blade passed refreezes! But most materials do not show this anomalous behavior and in fact have melting points that INCREASE with increasing pressure...iron is such an example.

The short answer: pressure. The melting temperature of any material (as well as the boiling temperature of any liquid) changes with the pressure under which it is put, and that change reflects the change in density of the substance in question. Water is unusual in that the solid form(ice) is actually less dense than the liquid form, so if you put ice under enough pressure, it will melt. Most substances, including the nickel and iron that the core is made out of, are denser when solid, and so putting the liquid under enough pressure will cause it to 'freeze' (turn solid, that is - it will actually get even hotter by releasing the energy that was keeping it liquid).

The outer core is under pressure of about three thousand kilometers of rock, the Earth's mantle. The inner core is under that pressure, as well as another two thousand kilometers of molten metal (the outer core). That difference is enough to freeze the inner core. If you took a piece of the inner core to the surface of the Earth, it wouldn't be liquid or even gas - it would be a plasma, since the temperature (8000 degrees C - hotter than the surface of the sun)is so high.

The short answer to that question is: Pressure.

The inner and outer core are made of the same material, chiefly the metal Iron, with small amounts of Nickel and some other lighter elements.

However, geologists have discovered through a variety of experiments that as the pressure on a solid material increases, its melting temperature increases as well. In the earth, pressure increases with depth below the surface of the planet. So for example, rocks that are molten at the surface of the earth (lava) at a certain temperature, would be solid at the same temperature at a greater depth below the surface, where pressure is greater. In the outer or liquid core the temperature of the Iron is great enough and the pressure not quite high enough for it to exist in a liquid state. As you increase the depth (and therefore the pressure) to the inner core, the pressure becomes so great that the melting point for iron is greater than the temperature of the core, and the iron is forced into a solid state.