Flyback Diodes are used with inductive loads like dc motors and relays. Lets use a relay for an example. A common relay has a 12v 120 ohm coil. In use it draws .1 Amps. When you turn off the power, energy is pumped back into the circuit briefly as the field in the coil collapses, equal to the energy used while energized. A reverse diode across the load absorbs this spike, preventing damage to the circuit powering the load. In our example, 12 Volts / 120 Ohms = .1 Amps, so we need a diode capable of handling .1 Amps at 12v. The common 1N4001 is rated for 1 Amp at 50 Volts, so this is more than adequate for this application.
Remember the diode is installed “backwards”, with the stripe facing the positive, not the negative as a diode would typically be used.