In the theory of electromagnetic radiation, it is not so
convenient to work with the electric and magnetic fields directly,
except for simple plane waves. It is more convenient to use the
"scalar potential" and "vector potential."
You are probably already familiar with the scalar potential: in
many situations, it is just the same thing as voltage. A
5-volt battery has a scalar potential difference of 5 volts between
its terminals. The electric field, in static situations (given the
usual potential conventions of electrostatics), is just given by
the spatial rate of change of the scalar potential, and it
points "downhill" toward regions of lower electric potential.
There is also a "vector potential" that has to do with
magnetism. This is a quantity with a magnitude and a direction: a
vector. In static situations, the magnetic field is related in a
somewhat complicated way to the rates of change of the vector
potential in various directions: essentially, it has to do with the
extent to which the vector potential swirls around a given
point.
If the potentials are changing with time, as in radiation, then
the relation between the potentials and the fields is more
complicated. But in either case, in size, the electric and magnetic
fields are proportional to the rates of change of the
potentials in space and time.
Now, if the potentials are defined in a certain way (what the
pros will recognize as a "covariant gauge"), the potential due to a
certain charge and current distribution is related to the charges
and currents in an extremely simple way.
Suppose there is a point charge somewhere in space, which moves
around. Then the scalar potential at some other place is directly
proportional to the charge, and inversely proportional to
the distance to the charge.
But it is not the distance to the place where the charge is
now; it is the distance to the place where the charge
was, at such a time that a signal traveling at the speed
of light from the position of the charge is just now getting to the
place where we're calculating the potential. The news about where
the particle is travels at a finite speed, the speed of light. This
is called a "retarded potential," meaning "delayed," because it
responds to the charge's position with a speed-of-light delay.
If there is more than just a point charge, then the scalar
potential can be calculated by adding up the retarded potential of
each little bit of charge.
The vector potential is related in exactly the same way to the
currents. Each little piece of current creates a retarded
vector potential that is proportional to current and inversely
proportional to distance, and the news about where the current is
travels at the speed of light.