What Is A Hall Sensor?

Bell Technologies Inc.,

A Hall sensor is a four-terminal, solid-state device capable of
producing an output voltage VH, proportional to the product of the
input current, lc,the magnetic flux density, B, and the sine of the
angle betweeen B and the plane of the Hall sensor. A reversal in
the direction of either the magnetic field or the control current will
result in a polarity change of VH. A reversal in the direction of
both will keep the polarity the same. By holding the control current
constant, the Hall voltage may be used to measure magnetic flux
density. Multiplication may be accomplish by varying both the
control current and the magnetic field..

Source ( pdf )
http://www.physics.brown.edu/physics/demopages/Demo/
em/demo/halleffect.pdf