the flyback (freewheeling) diode

An inductor — a relay coil, a motor, a solenoid — hates having its current interrupted. It is a flywheel for current: stop it suddenly and it lashes back with a huge voltage spike (V = L times dI/dt, and dt near zero makes V enormous) trying to keep its current flowing. That spike can be hundreds of volts and will arc switches or destroy the transistor that opened the circuit. The flyback diode, also called a freewheeling or catch diode, gives that trapped current a safe loop to die down in.

You wire the diode across the coil, reverse-biased in normal operation so it does nothing. The instant the switch opens, the coil's voltage flips polarity and tries to spike — but that polarity now forward-biases the diode, which clamps the coil's voltage to just ~0.7 V above the rail and lets the current circulate ('freewheel') around the diode-coil loop, decaying gently as the energy bleeds away as heat. The deadly spike is gone.

This is one of the most important protective tricks in practical electronics: any time a transistor or microcontroller pin switches an inductive load (relay, motor, solenoid, valve), it needs a flyback diode. A Schottky is often chosen for its speed and low drop. The only cost is that the current decays more slowly than it would if you let the voltage spike, so for fast turn-off (motor drives) people sometimes add a resistor or Zener in series to bleed the energy quicker.