Mutual inductance is superbly demonstrated in a transformer. Transformers are made up of two wire coils placed close each other such that current running in one coil can induce a voltage in the other coil without the coils touching. Power can be transferred without a metal connection with a transformer, and transformers can be used to increase the voltage from the primary side (the first coil) of the transformer to a higher voltage on the secondary side (second coil). Stepping up the voltage with a transformer is extremely common, as in transmitting power over long distances since higher voltages do not lose as much energy. Transformers are also used to step-down the voltage to lower voltage levels, which is why transformers are commonly found in electronics and power supplies. Additionally, transformers make a good buffer to isolate one circuit from another.
You might already know from grade school that electricity and magnetism are closely related. If one is present, the other will be present in some form or another. The kinetic energy in the movement of water is transferred into energy in the form of electricity. Turbines in water falling over a dam are used to turn magnets, which in turn induces electrical flow in wires that are somehow coupled with or coiled around the magnets. Motors, generators, and transformers all use the principles of electromagnetism and induced current to transfer energy. As previously stated, transformers are mutual inductors. This means that as current flows in the first coil, it creates a changing magnetic flux in the second coil. There’s a lot of formulas involving integrals, derivatives, differential equations, and more that explain the precise relationships between electricity and magnetism, as writ in the engineer’s language of mathematics. However, let it suffice to state that there is an induced Electromotive Force (EMF) in the second coil. Since electricity always has an association with magnetism, Electromotive force (EMF) can become Electromagnetic Interference (EMI) when induced current happens where it’s not wanted.
With signals at high frequencies, or radio frequencies (RF), mutual inductance becomes more of a problem than resistance because traces on a PCB, although not touching, can induce stray current where it’s not wanted or expected. In such situations, mutual inductance might also be referred to as “coupling” that creates “crosstalk.” Crosstalk refers to unwanted signals that develop between adjacent circuits, cables, or traces due to mutual induction. Therefore, it’s critical to shield cables and connectors from higher frequency signals.
Separating circuits with distance helps to reduce the mutual inductance caused by lines of magnetic flux, but two circuits separated in space tend to “find each other” magnetically better than if the two circuits are sitting on a plane. Two boards sitting on point (a.k.a. catty-corner, or diagonal to each other) will experience less coupling than when placed side-by-side. Designers today have less choice on where to place circuits and PCBs as components and products become smaller. Shielding boards from one other will work as long as the shield is grounded. Short wires will not create loops (inductors) like long wires will, and current, even induced current, will always look for the shortest path to ground, so make sure you create the shortest path to ground so you know where the current will flow. The shorter the trace/wire, the better they work (especially as your frequency increases), but only because a short wire creates less inductance. Grounding to avoid problems caused by parasitic capacitance and mutual induction is another discussion that is difficult to teach academically because the scenarios for encountering both are varied and many. Avoiding EMI through good design starts with some rules of thumb and improves best with experience (and an oscilloscope), even if that experience is borrowed from colleagues.
Recommended Reference: High-Speed Digital Design: A Handbook of Black Magic by Howard Johnson and Martin Graham