This field has the ability to influence materials which were sensitive to magnetism, like magnets or iron. All planets and stars, large or small, have a magnetic field. Its strength depended on the mass and materials of the object.
In 2267, the scope of the magnetic effect encountered when Lazarus and anti-Lazarus emerged from the alternative warp, was the detection of complete disruption of normal magnetic fields throughout the Milky Way Galaxy and beyond. At the epicenter of the event, the entire magnetic field of the solar system "blinked" out of existence, whereas the mass of the source planet attained zero gravity. (TOS: "The Alternative Factor")
Federation runabout hulls were made out of metallic composites which interacted with magnetic fields. In 2369, Chief Miles O'Brien upgraded a probe with a differential magnetometer and was able to detec the missing USS Yangtzee Kiang. (DS9: "Battle Lines")
Artificial magnetic fields, better know as electromagnetic fields, can be created and manipulated for a number of uses, including containing antimatter in antimatter containment pods, magnetizing gravity boots, and generating an electromagnetic pulse to jam communications. (Star Trek: The Next Generation Technical Manual, ENT: "Babel One", DS9: "Sacrifice of Angels")