What is spin of an electron?

Spin is a quantum number. Quantum number is used to define the state of an electron in an atom.

Quantum numbers:

1. Principle quantum number indicates distance of the electron from the nucleus
2. Azimothal quantum number indicates angular momentum of the electron orbiting.
3. When electron orbits in the orbital it creates a magnetic field which is expressed by magnetic quantum number.
4. Spin quantum number is an intrinsic magnetic field which arise from the spinning of the electron on it's own axis.
   

Things written above can't be taken literally. It's only poor analogy drawn between quantum and classical mechanics. From classical theory and experiment we know that moving charge (macroscopic) produce magnetic field. Charge is a fundamental property of matter, there is no question about it's existence. Now the question is whether it is true for fundamental particles like electron or proton. Do moving electron produce magnetic field? I think it does. Because magnetic field is a fundamental thing, if it is not produced by some fundamental action it can't arise at all. From that we can be sure that moving electron must produce magnetic field.

But there is a difficulty in saying that the spin of electron arise from rotating on it's own axis. To produce observed magnetic moment the equatorial region of the electron must rotate at speed more than that of light. And another point that electron don't spin in classical sense is that - to complete a period or make a complete revolution it must rotate 4 pi radian as opposed to 2 pi.

So here are the safe things to say -
1 . Electron has two magnetic field separate from each other.
2. One is associated with the shape of orbital and other is intrinsic.
3. Both of the them are quantized,
4. Spin quantum number can only take two values - +1/2 and -1/2.
5. Electrons in the same orbital must have different spin quantum number.
6. Because spin quantum number can take only two values associated magnetic moment has also two values. If set in a magnetic field it can either align with or against the magnetic field but can't do otherwise (say align in a direction 60 degree with the magnetic field). I don't know the answer why??