The magnetic field is one of the five fundamental fields that pervade space, along with electric, strong, weak and gravitational fields - although electricity and magnetism have been considered two aspects of one more fundamental field since the late 1800's.
At every point in space, the magnetic field has a value which is a vector, i.e. a strength and a direction.
The magnetic field can exert a force on a magnet, or a moving electrically charged object - including electrons, which make up currents. This effect is used in many ways, including electric motors. A changing magnetic field can effect stationary electrically charged objects - an effect used in electric generators.