What is the magnetic moment, and what does it have to do with the spin of the electron? So when an object spins (like the electron), it is said to have a magnetic moment. Now, I do not understand what they mean when they say that it has a magnetic moment.

When I did research, I saw this picture from which I assumed that the magnetic moment is nothing but the magnetic field of the electron. Is my this hypothesis wrong?
I also read that spin up and spin down refer to positive and negative magnetic moments. If this is the case, then clearly a magnetic moment is not a magnetic field.
So I am getting very confused as to what a magnetic moment for an electron means.
 A: An electron acts like a very small magnet. We say "magnetic moment" rather than "magnetic field" because a field is a local property (move further from the electron and the field gets weaker), while the magnetic moment is a property of the electron from which you can deduce the field at any point, and from which you can calculate the energy required to align the electron with an externally applied magnetic field, or the torque experienced by a particle whose spin is not perfectly aligned with a field.
A: It's that the electron has a magnetic dipole moment. It's akin to an electric dipole moment inasmuch as it generates a magnetic field that behaves similarly to an electric dipole field (falls off like $1/r^3$). Unlike electricity, which has net electric charge as a monopole moment, the lowest order moment possible in magnetism that obeys Maxwell's equations is the dipole moment. For more details about the magnetic multipole expansion go here. Note that the idea is that a multipole moment generates a multipole field of the matching sort, and any generic field can be approximated by a sum of multipole fields, in the appropriate region (e.g. outside of all of the charges/currents generating the field).
The physics 102 formula for calculating the dipole moment of a flat current carrying loop of wire is:$$\mathbf{\mu} = I A \mathbf{n},$$ where $I$ is the current, $A$ is the area of the loop, and the direction of the unit vector, $\mathbf{n}$, is fixed by a right hand rule. More generally, it is possible to show that the magnetic dipole moment is proportional to a charge carrier's angular momentum, and hence the connection to spin.
