silverstreakin has the basic explanation for you, it's slightly more complicated though, so for those interested, here goes:

As everyone discovers in a physic class, magnets can induce a current in a coil of wire as the magnetic field moves past the wire coil. Magneto type ingitions use this principle to generate a high voltage, low current spark without the need for an oustide power source.

On your lawnmower, your "coil" is actually a transformer with two sets of wires sharing a common iron core with arms that extend down close to the flywheel. As the magnet approaches the leading arm, a current begins to move in the primary winding, and continues to build until the magnet passes the second arm. At this point, the electric field in the primary winding collapses, which induces another current into the secondary winding. Since the coil is a transformer, the secondary winding has many more "turns" of wire than the primary winding, so the secondary winding is also called the "high tension side". The reason for this is because you can't gain or lose energy, but you can change it's state, so as your primary winding collapses, it's higher current energy is passed to the high tension coil at a much lower amperage, which means that the voltage increases proportionally with the ratio of turns of wire on the two windings. By now this high voltage energy is desperately wanting to find a ground source, and it now has enough voltage to do so by jumping the gap between your spark plug electrodes. All this activity happens in a fraction of a second.

A canister type automotive coil does all this in a similar fashion, except the energy given to the primary winding is provided by the car's battery instead of a traveling magnet.