The law is at the heart of an electronic component called an inductor. This is essentially a coil or solenoid. When the current in the coil charges, the change in flux through the coil generates an emf in the coil itself that tends to counteract the change in current - another example of the opposition implied by Lenz's law. This sounds a bit like inertia - a moving mass has inertia that resists any change in its velocity. This phenomenon is called the self inductance, since the changing field of a coil induces an emf in that coil itself.
Transformers operate by the principle of mutual inductance.
An alternating current is directed through a 'primary' coil. This creates a time-varying magnetic flux that induces an emf in a neighboring 'secondary' coil. This process is one of the main reasons that what you get out of the wall is AC rather than DC - it's hard to charge DC voltages, but it's trivial to charge AC voltages. Thus relatively small AC currents can be run through high voltage power lines with little dissipation, and then reduced to 100 VAC or 220 VAC using those funny gray things on the tops of power poles. Electric generators and alternators operate by induction using a coil and a permanent magnet.