what do they do?
They determine the power the motor receives in order to vary the thrust or lift from that motor, otherwise you would have on/off control, not a variable speed. In brushless motors, they provide the polypase voltage required to make the motor spin.
are they needed?
You cannot fly a quad without variable control of the motors and thrust
Isn't arming/disarming them a pain?
FYI, you don't actually arm the ESC, you are arming the APM control system, the ESCs are ready to run at power up. The ARMING is for safety and trust me, if you are asking these questions you need it.
how should they be used?
Depending on what type of motor, brushed or brushless, you STILL need a speed control to run it. Also you cannot mix and match motor types and speed controls for obvious reasons.
how many do I need?
You need one for each motor because that is the flight control system. Instead of servos and air vane controls to vector thrust, we just vary the motors individual thrusts.
As stated by others, brushed motor have a very finite lifespan measured in hours when pushed to high power levels required by multi-rotor aircraft. They simply are just not up to the job. We can go on for days, but trust me, just not worth even discussing motor theory. Brushless polyphase removes the mechanical brushes and fast wearing, failure prone comutator, removes the windings rotating on the armature which are under extreme heat and mechanical stress from centrifugal force (ever hear of a "thrown" winding"). Just say OUCH!
In brushless motors, the windings stand still and the permanent rare earth magnets are attached to the rotoating assembly, This arrangement has proven far supperior in every aspect to the brushed motor, from reliability, to all out performance, to total system efficiency. The brushed motor cannot compete on those fronts.
Others have given you the same reasons so sorry if any of that is repetative. Just to be clear, the entire reason for the multi-rotors is to use a simpler system rather than the complex linkages, adjustments, swashplate, systems of a conventional heli. Also, we gain some efficiency by not fighting torque with a tail rotor, so almost all of the energy goes to lift, not lift and torque, then fighting counter torque with a tail rotor. Yes, coaxial solves the torque problem, but still has mechanical linkages. Multirotor uses (typically) fixed propellor pitch and we just vary motor speed thus the reason why you need good speed control and really only polyphase can provide, as even a brushed motor can vary from motor to motor and that would not be good in this application.
This mechanical insanity is what we are trying to avoid with reliable and proven electronic speed controls and brushless motors. Below is a picture of a coaxial (counter rotating) rotor head with both upper and lower swash plate control. The main advantage is the increased lifting capacity and efficiency, along with stability for FPV or Camera platforms. Imagine adjusting that????? Complete site http://www.infinity-hobby.com/main/product_info.php?products_id=5392
+2 on NOT using brushed DC motors.
Below is a picture of the result of exceeding the maximum RPM of a brushed motor. This motor/generator was on a motorcycle I own that was the victim of a mechanical failure while the bike was running about 40 MPH.
What happens if your mosfet/switch shorts while at speed? (A normal failure mode for them before they burn open IF they burn open)
Guess what happens to the brushed DC motor?
You cannot control it anymore and it spins to the maximum the system allows and stays there until the energy supply is gone or the motor does what is seen in the picture, or the switch/MOSET burns/blows up, or some combination of the previous. Regardless the aircraft is going to do something you don't want it to do.
To mitigate this situation you would have to add enough failsafe electronics that the 'simple switch' idea is now capsized by the complexity of the safety circuitry.
Polyphase ESC systems are small, light, have built-in safety circuitry and are bascially a LEGO block for a quad project.
IF for some bizarre reason the ESC commanded the motor to run to infinity, the limit would still be the energy supply, the wiring, and the mechanical limit of the bearing and prop hardware. In a polyphase system, the motor can never reach the exact input instantly due to flux lag and friction.
I think the talking points FOR current technology ESC completey outweigh using brushed DC systems but, in the spirit of adventure and learning, build your quad the way you want to within the limits of your budget and see how it works. We will try to help you get it in the air.
There is no better teacher than experience. Ask the brushed DC motor below about that.
I just want to thank everyone here for giving me all this advice on what could go wrong is great, there are some things that I never even thought were a possibility, and I will be sure to add many more things to my design, and take advantage of whatever I can find out from the mistakes of others.
I couldn't even make an educated guess about this until I had this information, which is why I came here in the first place, to learn from all of you. Whatever I end up doing in the end, I know that it will be better because I'm not going into it blindly.