From what I know from various textbooks, pop-science shows and my classes, the earth's core is solid. But how does the concept of solid and liquid make sense at these high temperatures.
The Earth's core is both solid and liquid. The outer core is molten and produces currents of molten nickel/iron which generate the Earth's magnetic field in a dynamo effect, while the inner core is solid. The reason the inner core is solid is that it is under tremendous pressure, more so than the outer core. Scientists know this from the analysis of seismic waves which pass through the Earth.