The Hall effect, detected and described by Edwin Herbert Hall in 1879, arises when a small voltage appears across a conductor in the presence of a magnetic field. The field is transverse to an electric current in the conductor and to the lines of magnetic flux, which in turn are perpendicular to one another as is possible in three-dimensional space.
The ratio of the induced electric field to the product of the current density and the applied magnetic field is known as the Hall coefficient.

A Hall effect sensor takes advantage of the phenomenon. It responds to changes in the magnetic environment and is capable of outputting information regarding the strength of the magnetic field and its own distance from and position relative to that magnetic field.
In its most common form, the Hall effect sensor is a thin rectangular slab of P-type semiconductor material. A nearby magnetic field results in magnetic flux, which causes charge carriers, electrons and holes to migrate to opposite sides of the semiconductor. The bottom line is that there is a voltage difference across the device. When there is no magnetic field near the semiconductor material, the charge carriers (electrons, holes or ions) travel in straight lines as they move from one collision to the next.
However, in the presence of a magnetic field, these carriers follow a curved trajectory. As a result, they accumulate at the two opposite faces of the slab. Because of these concentrations, a small but palpable voltage difference appears across the material, perpendicular to the voltage difference that is applied by the power supply. This voltage can be measured and calibrated to indicate the existence and position of the magnetic field. As a sensor, the device has many applications and is widely used.
In most implementations, a south magnetic pole of sufficient magnitude causes the Hall effect sensor to output what is known as the Hall voltage. It is directly proportional to the strength of the nearby magnetic field. Typically the Hall voltage is small, in the microvolt range. But that level is sufficient to trigger integrated amplification so as to produce usable electrical signals.
A common application for a Hall sensor is at the output of a servomotor so as to provide speed and position information, enabling closed-loop control. A Hall effect sensor can be manufactured as a sealed unit so as to be highly resistant to vibration, heat, moisture and whatever contamination may be present in a hostile environment.
Thanks for your comment about how Hall effect sensors can help output information. I like how you said that it can charge carriers with magnets as well. If someone was considering Hall effect current sensors, I would assume that they would keep this post in mind.