"This is a computer system designed to prevent the nose of the Boeing 737-Max from pulling too far up and putting the plane into a stall when under manual control. It has nothing to do with the airplane's autopilot."
Nope nope nope nope nope
When machinery is under manual control, it should be under manual control. There is absolutely no reason at all for this system to automatically control the aircraft. For decades aircraft have had the capability to alert the pilot audibly and visually and to even announce recommended action to a potential stall condition as well as a plethora of other potential pilot errors. That's where it should end. The pilot should always then get to decide whether to follow that advice or not.
How the hell did people sit in a room and decide that it was fine to let the computer have the final say?
I can handle the risk of a pilot making a mistake, I know that other than in the rarest of cases they will tey very hard to correct that error to save their own skin.
MCAS is Boeing's solution to the problem of getting the 737 MAX certified as airworthy by the FAA (14 CFR Part 25 - AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY AIRPLANES). The 737 MAX replaced the engines with heavier, differently shaped, more powerful versions that needed to be placed further forward on the airframe. This increased the moment arm of the engine's thrust, which exacerbated the pitch-up when thrust was increased. This meant that at high angles of attack, increasing the thrust could stall the aircraft*. In order to pass the FAA's longitudinal stability requirement, Boeing came up with MCAS, which moves the stabiliser to provide nose-down pitch at high angles of attack to prevent stalling. Without MCAS, the 737 MAX would not have been certified to fly.
More information here: The Air Current: What is the Boeing 737 MAX Manoeuvring Characteristics Augmentation System (MCAS)?
And here: Leeham News: Boeing’s automatic trim for the 737 MAX was not disclosed to the Pilots
It operates when the aircraft is being flown 'manually' (i.e. not by the Auto Pilot) with flaps up, because without it, the aircraft would not be certified as airworthy. It is there to prevent unwanted handling characteristics becoming a problem, but that works only when MCAS is receiving good data. You can fly a Boeing 737 with electrically assisted trim turned off, as there are manual trim wheels connected via cables to the stabiliser trim mechanism. They move when the electrical trim operates. Manual operation requires 50 turns per unit of trim (250 turns from full up to full down), and if the stabiliser is experiencing significant aerodynamic loads, can require some effort to move.
So, if you are flying with flaps up (i.e. not configured for landing), without autopilot, MCAS is in operation. If the MCAS system is incorrectly told there is a high Angle-of-Attack, it will automatically command Nose Down trim until the AoA falls to a level that the MCAS system programming is set up to regard as not needing the correction assistance. If the AoA doesn't change by enough, it will continue to command Nose Down pitch. It the pilot uses the toggle switch on the yoke to manually control the electrically assisted stabiliser movement, MCAS backs off for a few seconds, but will resume after a short period. If you switch to autopilot, MCAS is disabled, and if you extend flaps it is disabled. However, if there is an airspeed mismatch between the pilot's and co-pilot's instruments, autopilots generally disengage. As the airspeed is calculated from a combination of data from the pitot system and the AoA sensors, if AoA is wrong, airspeed will be wrong.
If you are at the point where the stabiliser's nose down trim setting exceeds the elevator's authority to bring the aircraft's nose up, you have a problem (at this point, it will probably require both the pilot and co-pilot pulling as hard as they can on their respective control-yokes simultaneously). Disabling all electrically assisted trim at that point may put you in an unrecoverable situation, as you may might be unable to manually alter the stabiliser pitch setting fast enough to get out of the dive. If you are using all your strength to pull on the yoke, you don't have any hands free to rotate the trim wheels.
If the incorrect operation of MCAS is recognised at an early stage, it is easy to recover. If you leave it too long, it might not be possible to recover.
I am not an expert, so I may have got things wrong. Corrections are welcomed.
*This is simplifying things a bit. The shape of the engine nacelle also provides additional lift at high angles of attack compared to the previous engine, so even without extra thrust, pitching up can be less benign than you expect. MCAS is there to ensure the combination of the airframe and handling systems meet the handling rules - it is meant to provide predictability.