whats not to get? change in current cause a change in magnetic field which cause a current that opposes the initial current. This keeps a circuit from lighting up instantly, it also keeps the circuit from dieing instantly.
We've all probably heard induction in action. A vacuum cleaner, for example, wont just start ON, it whirls up. As well, if you where to pull the plug on a running vacuum, you would see sparks from the plug as well as hear the vacuum whirl down. That is induction in action.
Another neat way to see induction, that you guys may not know about, Take a metal sheet. Use aluminum or copper, something that is NOT ferromagnetic. Grab a strong magnet, tilt the sheet at an angle and let the magnet slide down it. You will notice that the magnet doesn't free fall to the ground, instead it slowly crawls. This is because the change in magnetic field is causing a current in the pan which causes a magnetic field that opposes the change in magnetic field! That is induction (well, eddy currents).