Use potentiometer to control motor's speed
Ah, now I see. Your confusion in this case is perfectly understandable. They threw a couple of capacitors into the circuit without explaining why they were added in the first place. In order to understand why capacitors were added you need to go a little deeper into electronics theory, specifically capacitance and inductance, what they are and how they work.

Inductance is, to put it succinctly, resistance (not related to the resistance in resistors, measured in ohms) to change in current by sacrificing or absorbing voltage. If current is 0, then inductance will try to keep it at 0, if at 1A then it will try to keep it at 1A, and so on. Inductance is caused by the magnetic fields generated by electricity flowing through a conductor, and hence every conductor exhibits some measure of inductance. (Coils have much higher inductance though, since the magnetic fields of the loops reinforce each other. And a "core" material such as ferrite or iron intensifies the magnetic field.)

Now, this isn't a large problem if your conductors are short, but as they get longer their inductance can cause power issues. Sudden power demand increases are unable to be accommodated because the supply can't put the increased current through the inductance quickly enough. This is where capacitance comes in.

Capacitance is resistance to change in voltage by sacrificing or absorbing current. When something tries to reduce the voltage either through power consumption or because of high-speed switching, capacitance holds the voltage as close to constant as it can by pulling or dumping electricity out of or into the circuit. Capacitance is caused by charges between two conductors attracting each other through a non-conductive material.

So what happens is that a circuit needs bursts of power to work, and if the wires connecting the supply to the circuit have too much inductance then the circuit will be starved of power. We balance this by placing a capacitance close to the circuit so that it can supply power to the circuit for the short time while the supply is busy overcoming the inductance of the wires.

The servo, being a mechanical device, needs a decent amount of power. We put a bulk capacitor near it on the supply lines to help provide this power. The analog input connected to the potentiometer needs much, much less power, so the inductance there isn't a problem and we forgo the capacitor there.