Magnetic stirrer with hot plate
Most of the things to be told about magnetic stirring are already in Rons comment. A rotating magnetic field is induced by a rotating permanent magnet inside the hot plate magnetic stirrer. This field drives the magnet inside your reaction flask. To ensure chemical inertness in most situations the magnet is coated with PTFE (Teflon) or protected by a thin layer of glass. Magnetic stirring can replace traditional mechanical stirring is most situations and has many benefits over it: it does not require an additional inlet to the reaction flask, which is very handy for reaction under reduced pressure and is also more easily adjustable to different scales due to the possibility to replace the magnet in the reaction flask. Two exceptions are 1) very large/very viscous reactions or reactions in which excessive amounts of solid are present 2) reactions that involve ferromagnetic compounds that interfere with the rotational movement of the magnet inside the flask (as in Urushibara nickle catalyst preparation).

Vogel has a section on reaction heating and stirring in which this and more is discussed extensively. See pages 71-80.