The magnetic field of the Earth is a result of a huge electric current that flows in the molten portion of the Earth's outer core.
There are two basic ways to create any magnetic field. One can have a permanent magnet like a bar magnet which has a magnetic field or one can have an electromagnet, like a solenoid, and the flow of electric current produces the field.
Inside the Earth, there is a very large current.
The complete explanation requires a description of what causes the current. This has been a matter of scientific conjecture for five centuries. The most favored explanation is called the the dynamo theory and describes the origin of the current circulating in the Earth's core.
The Earth's core has two parts, an inner core that is solid and an outer core that is liquid. The core is made primarily of iron and nickel and is very hot and under great pressure.
The inner core has a radius of about 1,000 km (700 miles) and the liquid part extends another 2,000 km (1,400 miles) until the Earth's mantle is reached at a depth of 5,000 km (3,000 miles) beneath the Earth's surface. The core is very hot, about 5700 K (5400 °C), and the pressure at the center is enough to make the inner core solid.
The nickel iron mixture of the core is a very good conductor of electricity and the current causing the Earth's magnetic field resides there. There is, of course, electrical resistance and if there were not something causing the current, it would disappear in a few thousand years.
The dynamo theory explains the current is caused by the motion of the liquid part of the core. As the liquid move through the existing field, like any conductor moving through a magnetic field, a current is induced in the moving conductor. That adds to the current already present and keeps the current from decaying due to natural electrical resistance of the medium.
The liquid in the core is in motion for two reasons. First, there is convection in the core. The inner core is much hotter than the surface, so hot fluid at the inner core tends to rise towards the cooler mantle above it. In addition, there is a coriolis force due to the rotation of the Earth. (This is the same force present in the atmosphere of the Earth that is responsible for the general trends of winds around the globe.) The liquid motion in the core forms as roughly stable pattern, replenishing the current and maintaining the field which. As a result, this is a self sustaining process, with the field causing the current and the current causing the field.
Other Issues:
The dynamo theory requires a lot of detailed information and complex calculation to go from the qualitative picture presented above to a quantitative description of the properties of Earth's magnetic field. The research on the theory and the calculations of predictions is quite an active enterprise.
There are furthermore other aspects of the field that require explanation, such as the fact that the north and south poles switch positions (pole reversal) sometimes and this may happen every few million or even few thousand years.
The general shape of the Earth's magnetic field is very much like a bar magnet field. The shape is said to be a dipole field more or less. But the general shape has a great many details and anomalies where the strength and direction of the field are not so simple. This is only partly caused by variations in the thickness of the mantle layer.
Finally, it is know that Earth is not the only planet with a magnetic field. Several other have, or in the past had, a magnetic field. Even some moons in the solar system show evidence of present or past magnetic fields. It appears that the mechanisms that create a planetary magnetic field are quite natural and it happens all the time.
Many aspects of geomagnetism are still under investigation.
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