Thats why I am asking you to tell me a case where you can use BEC.
Maybe it would be more explanatory for you if you knew a bit of history and why BECs came about:
Back in the dark ages of the RC hobby, there would typically be two separate batteries used on the vehicle being controlled. One battery would be for the receiver and the servos, and would typically be a 6 volt battery composed of four alkaline AA batteries (and latter, 5 cell NiCd or NiMh); the other battery was typically larger in size and voltage output, meant to drive the main propulsion motor. Control of speed was either done in an electro-mechanical manner - via a servo switch resistors to control voltage to the motor - think of it as a mechanically switched voltage divider with large resistors - or sometimes a high-wattage potentiometer. Later, electronic PWM controls were introduced.
The problem was that - mainly for electric flight airplanes and helicopters - having two batteries on-board meant that you had to lift extra weight, which cut down on flight time. So some method was needed to convert the higher voltage main battery to a voltage level sufficient for the receiver and the servos (again, generally 6 volts).
Enter the BEC: Simple BECs were simply 7806 linear voltage regulation circuits, not unlike the 5 volt regulator on the Arduino. These weren’t the most efficient of devices - plus you had to have heat-sinking and such to be able to handled the needed current of the servos. As technology improved, though, switch-mode BECs became more commonplace; although you can still find el-cheapo linear regulator BECs around, most are of the switch mode variety.
What this meant was that by using a BEC, you could eliminate the second battery, and power everything off the main battery - saving weight and increasing the running time. It brought up it’s own issues, though - because as the system was now using a single battery for everything, if the battery got too low - the BEC might not work - and control of the device would be impaired. When that device is an RC airplane or helicopter, you can imagine that would be a bad thing! So, further systems had to be devised to sense this condition, and shut off the main power source while leaving the controls intact. Further improvements were made for audio feedback for the operator of an impending shutdown, among others.
So - you will may certainly need to use a BEC on a quad-copter depending on what you are planning on running on that machine. If it’s just a basic quad, then you might not need it at all - depending on the voltage of your main battery, what voltages your radio receiver or whatnot can tolerate, and how large of a voltage drop to your controller system (Arduino or arduino-based, I presume) will be needed - and whether the on-board voltage regulator of that device can handle the drop and any generated heat.
That’s something you’ll have to figure out.