* Power supplies are limited in the speed of their response to changes in current demand.  When there are sudden changes in demand, such as when transistors quickly turn on or off at MHz speeds as they do in digital circuits, the power supply voltage briefly dips below or spikes above its nominal voltage.
* Moreover, the conductors that carry current from the supply to the devices it powers have inherent inductance - that is, the wires resist changes in the flow of current and as a result, the voltage at the far end of the wires dips and spikes in reaction to changes in the flow of current through them.
* These variations in supply voltage can cause problems in the some devices, particularly if those devices must measure small changes in voltage such as analog sensors.  If the noise is severe enough, it can even cause problems for digital devices that need only distinguish between binary voltage levels.
* Suppression of this sort of noise is typically accomplished by adding a small decoupling capacitor in parallel with the supply pins of each current-consuming device.  The decoupling capacitor is placed as close to the device's power input pins as possible.  The capacitor serves as a reservoir of charge: when the supply voltage dips, the capacitor releases some of its stored charge back into the circuit and when the voltage spikes, it stores some of the excess current.  As a result, the capacitor effectively smooths the voltage spikes seen by the device it is decoupling.
* The inductance of the supply wires/traces aid this process by preventing current being supplied by the capacitor from flowing away from the current consuming device back towards the supply.  The series inductance of the wires combines with the decoupling capacitor to form a low-pass filter that effectively smooths out the high frequency digital noise on the supply lines.

* There are many different types of capacitors and their internal series resistance varies considerably with their chemistry and construction.  A capacitor's series resistance is often referred to as Equivalent Series Resistance or ESR.  In your kits, there are a few aluminum electrolytic capacitors; these typically have high capacitance (10s to 1000s of uF),but also relatively high ESR (5-40 ohms).
* ESR literally resists the flow of current into and out of the capacitor which works against our decoupling objective of rapidly storing or releasing charge when needed.  The lower the ESR of a decoupling capacitor, the better.
* Although they have less capacitance, ceramic capacitors are typically used for decoupling high-frequency digital noise because they have very low ESR.  The small capacitance means they can't supply power for very long, but the low ESR means it can supply the power very rapidly.  This is perfect for the very high frequency noise in digital circuits.  If you examine any digital circuit, you will find a small ceramic decoupling capacitor near the supply input of *every* device in the circuit.  Ceramic capacitors ESR is typically less than 0.1 ohms.
* Larger aluminum electrolytic capacitors are used to smooth low-frequency noise such as the 60Hz from AC power lines.  The power supplies that convert 60Hz AC power to the low DC voltages used by our circuits typically include several large electrolytic filter capacitors placed in parallel (to reduce their ESR).  These filter capacitors can store enough charge to keep supplying power for the relatively long periods (ms) when the AC supply dips to 0 which happens 60 times a second!

[[Image(http://images.fineartamerica.com/images-medium-large-5/smiley-the-water-tower-steve-augustin.jpg, align=right, width=200)]]
Using the water analogy, a decoupling/filter capacitor is like a water tower.  When there is constant water pressure (pressure is analogous to voltage), water is pushed up to a certain height within the tower.  If there is a sudden demand for water (water flowing is analogous to electrical current) such as a factory opening a big valve, the water pressure at the factory will momentarily drop until more water being pumped into the system from the distant water treatment plant can reach the factory.  Placing a water tower near the factory can compensate for the drop in pressure: when the pressure starts to drop, the water in the tower will flow back down into the system, keeping the water pressure steady until either the water in the tower is exhausted or the water from the treatment plant reaches the tower and refills it.  This is actually why we have [https://en.wikipedia.org/wiki/Water_tower water towers].

The capacitance of a decoupling capacitor is analogous to the volume of the water tower's storage tank; the series resistance is analogous to the diameter of the pipe leading up to the tank (higher resistance = smaller diameter).  Obviously the smaller the pipe, the slower the tank can fill/release.  A big tank with a narrow pipe (electrolytic capacitor) is fine for managing long slow variations in water pressure over long periods.  A small tank with a fat pipe (ceramic capacitor) can respond more quickly but only for a short time.

You can learn more about capacitors for decoupling and other applications [https://learn.sparkfun.com/tutorials/capacitors/application-examples here]