Earth´s inner core and outer core are both made of an iron-nickel alloy. The state of matter (solid, liquid or gas) of a given material depends on its temperature and pressure. Most materials, including iron and nickel, change from liquid to solid at lower temperatures and/or higher pressures. It´s easy to understand going from a solid to a liquid at higher temperatures because we are all familiar with ice melting on a warm day. Why do materials change from liquid to solid at higher pressure? For almost all materials (except water), atoms are packed closer together in the solid state than in the liquid state. So when you squeeze the atoms together with high pressure the material changes from liquid to solid.

As you go deeper in the Earth both temperature and pressure increases. Although the inner core is very hot, it is solid because it is experiencing very high pressure. The pressure in the outer core is not high enough to make it solid.