If you have an inductive load like a solenoid it stores energy in it's magnetic field. When your driver switches off, the stored energy needs to go somewhere and the voltage at the coil terminal rises until it does go somewhere. A correctly connected catch diode is a common solution as it clamps the voltage to the supply and returns the stored coil energy to the supply. As the diode 'catches' the stored energy, it is often called a catch diode.

Other solutions are possible, so you don't need the diode if you do something else with the energy. It is possible to use the drive transistor to dump the energy by turning it on a a bit when the coil terminal voltage is very high.

If you don't do anything the high voltage spike will probably exceed the drive transistor voltage rating and blow it up, either quickly or slowly.