Impedance matching is a technique required because equivalent amounts of energy can take many different forms, such as low power for a long time, or high power for a short time. In electronics, the term "impedance" is most often understood in terms of an ohms law tradeoff (higher current at lower potential or lower current at higher potential), and the related formulas are easy to find. But the requirement to match impedance is easier to grasp if you understand how energy could be transformed from one form to another and why that would be desirable.

Consider a system in which we have raised 100 baseballs to a height of 10 centimeters. The amount of potential energy stored in this system is equivalent to the energy in a system with a single baseball raised to a height of 10 meters. We could say that these systems, while storing equivalent potential energy, would have a different kinetic impedance when the energy is released. Imagine how different it would feel to be laying underneath a blanket of baseballs dropped from a few centimeters versus standing underneath a baseball dropped from several stories! One would be uncomfortable, the other, barely survivable. This is the impact that mismatched impedance can have on an electrical device.

Like baseballs, electrons in their orbitals have a certain potential energy "voltage" relative to another nucleus. This energy is released (electrical current flows) when there is a conductive path for electrons at a higher potential to move to a lower potential. A system with 10 billion electrons at 1 volt potential has the same energy as a system with 10 million electrons at potential of 1000 volts, but the one with the higher voltage would have proportionally less current (fewer electrons) than the one with the lower voltage. We would describe these two systems as having different electrical impedance.

In practice, electrical impedance is more complicated than a simple ohms law exchange because of the wonderfully useful property that impedance varies with frequency in all natural materials. This makes analysis less straightforward, but allows us to build filters.

If "electrons with potential" seems abstract, it can be conceptually worthwhile to examine the many analogs to impedance matching in the mechanical realm which are easiest to see when a natural or convenient energy source is transformed into a more useful form. No energy is created (indeed, energy is lost to heat due to inefficiencies); only the impedance is transformed, as we see in the following examples:

An automotive transmission is just an impedance transformer, taking the engine's optimal energy output at 1500-2000 RPM at low force and delivering it to the wheels at a lower RPM with higher force. The transmission matches the output impedance of the engine to the impedance of the car on the road so the engine doesn't stall under too high a load or burn too much gas under too low a load.

A butter knife is an impedance transformer (transforming the low pressure in your hand across the large area of the knife handle into 100X the pressure across the tiny 1/100th area of the blade.) The knife matches the pressing impedance of your hand to the slicing impedance of the butter.

A nut-cracker is an impedance transformer that transforms your hand's low force over a long distance into a very high force over the very short distance required to crack the nut. It matches the impedance of your grip strength to the cracking impedance of the nut.

An electrical utility transformer is an impedance transformer, transforming high-voltage low current into low voltage, high current. It matches the impedance of the utility line to the impedance of your toaster.

A hydro electric dam usually takes the high cross sectional area and low speed water flow of a river and chokes it into a single point with a much lower cross sectional area and a much higher speed where it can drive a turbine. The dam transforms the impedance of the river to the impedance of the turbine.

Even an air conditioner compressor could be said to be an impedance transformer; the coolant starts at room temperature and at a regular volume. Compressing the coolant increases its thermal potential while decreasing its volume. When the higher potential energy is radiated out through the exchanger coils, the coolant is cycled back inside and decompressed, but since it has lost energy to radiation, it is cooler. The air conditioner matches the impedance of the coolant to the thermal radiation impedance of the exchanger coil.

With the exception of the compressor example, all of these devices are simple and passive: some gears, a knife, a lever, some coils, a funnel... impedance transformers are everywhere, doing the simple and passive task of matching the form of energy you have into the form that you need.