While the ignition is "on" your alternator is in the charging mode. You have a rotating coil - the rotor, within a stationary coil - the stator. As the rotating coil rotates its magnetic field crosses the poles of the stator, generating alternating current in the stator. Diodes in the alternator convert it to direct current to run the electrics and charge the battery. While the alternator is doing this the magnetic field of the stator collapsing opposes the field of the rotor. Thus, the effective electric current in the rotor varies with the rpm and stator load. If memory serves me, you usually have about 4VDC coming from the voltage regulator to the rotor coil.
If you leave the key on, but the tractor not running, the rotor coil may not have a proper magnetic field, and it will just sit there and cook. Thus, you can get smoke. Eventually you may burn it up.
On a normal car engine, my dad always said you shouldn't leave the ignition "on" because if the points were closed the high voltage coil for the spark plug would burn up. Same general idea.