Electromagnetism is the physics of the electromagnetic field; a field encompassing all of space which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. The magnetic field is produced by the motion of electric charges, i.e. electric current. The magnetic field causes the magnetic force associated with magnets.
The term "electromagnetism" comes from the fact that electrical and magnetic forces are involved simultaneously. A changing magnetic field produces an electric current (this is the phenomenon of electromagnetic induction, which provides for the operation of electrical generators, induction motors, and transformers). Similarly, a changing electric field generates a magnetic field. Because of this interdependence of the electric and magnetic fields, it makes sense to consider them as a single coherent entity — the electromagnetic field.