Hall effect gimbals use a hall effect sensor which is an electronic component that measures magnetic fields. In the gimbal a magnet passes over the sensor and it measures the magnetic field and that is used to determine the position. These are less prone to wear and are more accurate.
Regular gimbals use a potentiometer which is a physical sliding mechanism and can wear out over time.
The difference is in how the gimbal position is sensed and reported to the processor in the transmitter. The two main types are potentiometer and hall effect gimbals, but in both types, the fundamental mechanism holding the gimbal and allowing it to rotate is the same.
Potentiometer (aka. pots)
Potentiometers are resistors which change their value depending on the location of the wiper along the resistive strip inside them. In a RC transmitter, the wiper is connected to each axis of the stick. The processor in the transmitter reads an analog voltage from the potentiometer and translates that to the axis' value.
A hall effect sensor also reports an analog voltage, but this time based on the strength of the magnetic field it senses. A magnet is attached to each axis of the gimbal and a hall effect sensor is placed on each side of the frame of the gimbal. The movement of the magnets either closer or further from the hall effect sensor registers as a changing value for the axis.
Potentiometers are generally less precise than hall effect sensors and tend to drift over time, leading to a need to calibrate the center point of each axis every once in a while. This doesn't need to be done with hall effect gimbals.