Experienced builders are well acquainted with many ways to reduce several functions to a single control axle, but the concept is important enough to present it to Technic beginners. Namely, typical approach, which works just fine for majority of MOCs, uses one control axle (or a motor) for each function. However, mobile and remotely controlled models often set strict limits on the number of electric components one can use, and in such situations it is necessary to go for alternate solutions - among which this differential-ratchet-gearbox system is just one of possibilities.
A careful look at the photos should reveal at least a little bit of how this system works ― but let's describe it component by component anyway. The input axle, in this case attached directly to a motor (A) is directly linked to a differential (B) master gear. Each of its two outputs leads to ratchets (C) that limit the rotation in different directions. This twin-ratchet setup ensures that the different directions the input axle is rotated are split among two exiting axles; this can itself be a useful component.
One output axle drives the input of a simple gearbox (D) which, in this case, has three output gears, though designs with four or more shouldn't present a problem. However, there is only one sliding intermediate gear, ensuring that the input rotation can be linked to only one output axle (E) simultaneously. Of course, the other axle from the differential controls the movement of this gear. In this case, it is done with a simple worm gear, spur gear and an off-center set control beam (F).
In other words, driving the motor in one direction changes the active output axle of the gearbox in the 1-2-3-2-1 order. Running it in the other direction transfers its motion to the selected active axle. Of course, the entire system can be built more compact in practice ― this display version was designed to avoid the components being obfuscated.
There are drawbacks one needs to be aware of, of course ― most importantly, the output axles rotate in one direction only (though, if they control a linear motion, the aforementioned off-center set beam connections can help). This system also allows the unlinked axles to rotate freely in one direction, and introduces some friction (thus reducing available torque). It's too large to cram comfortably in smaller models, and finally, it's somewhat noisy. But in certain situations, the benefit of controlling everything with just a single input axle, i.e. one motor, easily overshadows these remarks.
Venturing a little further into theory, it is conceivable to attach each of the output axles to off-center linkages that control Power Function switches connected to the motors attached to further such systems, squaring the number of available output functions (output axles). However, such system would be incredibly cumbersome to use.
Finally, a few auxiliary photos without labels, and a video: