Magnetic force is what arises from magnetic fields. Magnetic fields may arise form magnets (it is strictly not a source), steady electric currents or changing electric fields.
A magnetic field exerts magnetic force on charged particles given by
An interesting application is in the case of Aurora borealis, which is a splendid display of colors on the night sky near the north poles.
What happens is that charged particle from sun rays get trapped in the earth's magnetic field and move in a helical trajectory, they then ionize the gases such as Oxygen and Nitrogen up in the atmosphere. The ionized gaseous atoms then radiate light of discrete wavelengths. This causes the splendid display of colors as we see it.