To understand a magnetic dipole you have to understand the magnetic field that is created around a conductor which is carrying current: it deflects a magnet (compass needle, for example) at right angles
to the direction of current flow.
This site has an image illustrating this:
The light blue vertical rod at the center is the current carrying conductor. The darker blue rings with arrows around it show the apparent circular configuration of the magnetic lines of force that come into being around the conductor when current flows. To the right you can see a red and green compass needle; red for north, green for south. It is pointing at right angles
to the direction of current flow. If we were to place it on the other side of the conductor it would continue to be deflected at right angles to the current flow, but north would be the opposite direction than it is on the present side. The north and south poles seem to go in circles around the conductor.
Now, if we make a loop of that current carrying conductor, those magnetic rings configure themselves like this:
and what we see is that on top of the loop (I say "on top" since it is oriented horizontally in the illustration) all the north-pointing arrows are now curving into
the center of the loop. On the bottom they are pointing out and around. This is what makes the north and south poles of a magnet. Once you understand this you can see that a magnetic monopole is simply not possible, and also that there is no need for two different charges to make a dipole.
Dave explained in a practical way why the electrons in certain atoms amount to current flowing in a loop and allow those elements to give rise to magnetic fields.