This field has the ability to influence materials which are sensitive to magnetism, like magnets or iron. All planets and stars, large or small, have a magnetic field. Its strength depends on the mass and materials of the object.
Federation runabout hulls are made out of metallic composites which interact with magnetic fields. In 2369 Chief Miles O'Brien upgraded a probe with a differential magnometer 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 containmnet 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")