Short answers, pulled from the story.
A magnetic field is a physical property of space that quantifies the magnetic influence at a given location. It deflects moving electric charges, applies torques that twist magnets into alignment with the field, attracts or repels magnetic materials such as iron, and induces electric currents when it changes over time.
The B-field, or magnetic flux density, directly causes magnetic forces, torques, and induction; it is measured in teslas. The H-field, or magnetic field strength, is measured in amperes per metre. Inside a vacuum they are equivalent, but inside a material the two differ because the material's magnetization contributes to B but not to H. Lord Kelvin first distinguished them in 1850 and coined the term permeability for the quantity relating them.
Hans Christian Ørsted demonstrated in 1820 that a current-carrying wire is surrounded by a circular magnetic field. Andre-Marie Ampere then showed that parallel wires with currents in the same direction attract and repel when currents oppose, and Jean-Baptiste Biot and Felix Savart announced the law governing the force that a straight current-carrying wire exerts on a nearby magnet, also in 1820.
Between 1861 and 1865, James Clerk Maxwell developed and published the equations that unified all of classical electricity and magnetism. His 1865 paper, A Dynamical Theory of the Electromagnetic Field, completed the set of equations and demonstrated that light is an electromagnetic wave. Heinrich Hertz experimentally confirmed this in papers published in 1887 and 1888.
Earth's magnetic field creates a magnetosphere that shields Earth's ozone layer and the rest of the planet from the solar wind. The field is generated by convection of liquid iron alloy in the outer core through a dynamo process. Its poles periodically reverse orientation, with the most recent reversal occurring 780,000 years ago.
The largest magnetic field produced over a macroscopic volume outside a laboratory was 2.8 kT, achieved at VNIIEF in Sarov, Russia in 1998. In a laboratory setting, researchers at the University of Tokyo produced 1.2 kT over a macroscopic volume in 2018. Magnetars, naturally occurring neutron stars, produce the strongest known macroscopic magnetic fields, ranging from 0.1 to 100 GT.