The electromagnetic
field is understood to be the
electric field E together with the
magnetic field B, in
classical electromagnetism. The two constituent fields are of course field in their own right, but it is convenient to think of them as a single object whne you consider that
Maxwell's Equations say that the two are interrelated (at least when they are time-dependent). The
classical motion of a particle in an electromagnetic field is determined by the
Lorentz Equation.
Relativistic considerations of the field (ie. when
Special Relativity is taken into account) show that is is natural to view both the constituent fields as parts of a single object, called the
Maxwell Tensor field.