The brain that never gets to rest
A multirotor is inherently unstable. Left with all rotors at exactly equal speed, tiny manufacturing differences, a gust of wind, or an uneven payload will cause it to drift and eventually flip. There's no passive stability the way a fixed-wing glider has some. That means something has to actively hold the drone level, continuously, for the entire flight, and that something is the flight controller.
The flight controller is a small onboard computer running a tight control loop, typically hundreds to over a thousand times per second. Each cycle it reads sensor data, compares the drone's actual orientation to the desired one, and issues corrected motor speed commands. If that loop stops or lags too much, the drone loses stability almost immediately, which is why flight controllers are dedicated, real-time hardware rather than general-purpose computers running other software at the same time.