Its a conductor that detects a magnetic field and the movements of said conductor changes the voltage induced. It essentially means theres no physical potentiometer, which is the usual type of analog sensor in most controllers. These can wear out faster, leading to stick drift, inaccuracy, and other issues. Since Hall Effect sensors have no physical contacts to induce a voltage signal, they can last much longer and tend to be more accurate.
The hall effect uses a semiconductor and a magnet. When the magnet on the joystick is moved it generates a voltage in the semiconductor. This is preferable to using variable resistors because there is no contact and no significant moving parts to wear out. They are cheap, reliable and potentially higher resolution.
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