Think of the ESC as a replacement for the throttle servo.

Now, in the case of a nitro or gas plane, the throttle SERVO is where the electricity is needed, and the engine takes its power from the ignition. So your batteries just drive the servos and receiver, none of which draw massive amounts of current.

In an electric plane, the ESC performs the same function of the throttle servo, which is control, but it also PROVIDES all the current.

The ESC connects to the motor, a battery (which drives the motor and the internal electronics), and the receiver, which controls the ESC.

So the simplest (electrically speaking) setup would be to have the ESC wired to the motor, a big fat battery, and then plugged into the receiver which is being powered (into its "batt" connector) from a completely separate battery.

Now, thats simple but but practical, since you now have 2 batteries in your plane or car.

The receiver cant power the ESC since it cant handle the high currents, so it makes sense to make the ESC power the receiver in addition to taking commands from it. Thats what the BEC does, it allows the receiver to be powered by the ESC.