Answer:  This
is explained, in general terms, in the Introduction
to Geomagnetism page. Briefly, then, as the
result of radioactive heating and chemical differentiation, the outer
core is in a state of turbulent convection. This sets up a process which
is a bit like a naturally occurring electrical generator, where the convective
kinetic energy is converted to electrical and magnetic energy. Basically,
the motion of the electrically conducting iron in the presence of the
Earth's magnetic field induces electric currents. Those electric currents
generate their own magnetic field, and, as the result of this internal
feedback, the process is self-sustaining, so long as there is as there
is a sufficiently large energy source. The depiction of the geodynamo
shown here is only schematic; in fact, the fluid motion and the form of
the magnetic field inside the core are still the subject of intensive
research.
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