Look as a capacitor as a short term battery. It takes and holds a charge and gives it up on demand. It doesn't retain a charge for long. These are useful if you are using a motor or servo with a high power consumption that leaves the receiver starving for juice.

A BEC is a Battery Eliminator Circuit, it is meant to replace a receiver battery pack by taking power from the main motor battery and reducing the voltage for the receiver and servo. This is built into almost all modern Electronic Speed Controls. Generally the internal BEC reduces the voltage to 4.8 to 6V at 2 to 3 amps.

Some ESC's have BECs that can not handle a 3S (11.1V) lipo battery and in this case you use an external BEC as you pictured. An advantage of the CC BEC is that you can set the output voltage but its default is 5V.