(Also called “intrinsic angular momentum” or “inherent angular momentum”). Quantum Spin is a property of subatomic particles. While spin was originally thought of as a particle twirling around its axis like a toy top, this is no longer considered accurate. However, physicists continue to speak of spin as some kind of rotating motion. This video suggests one possibility: Electron spin.
Particles spin either up or down. And they spin left or right. So, there are two types of spin: 1) up/down, and 2) left/right. I can’t give a good description of Spin Left/Right, but what follows is a description of Spin Up/Down.
Seth Lloyd, one of the inventors of the quantum computer, uses the analogy of a twirling top for the benefit of a lay audience. He describes Spin Up/Down this way: “If you imagine a clock sitting face-up on a table, ‘spin up’ is counterclockwise and ‘spin down’ is clockwise. A convenient way to think of ‘up’ or ‘down’ spin is to curl the fingers of your right hand in the direction that the proton or neutron is spinning. Your thumb will then point along the axis about which it spins, and the direction your thumb is pointing in defines the ‘direction’ of spin—that is, up or down.” 
Problems with the spinning top analogy
When physicists calculated how rapidly electrons must be spinning, they realized that if electrons spun on their axes, they would be spinning faster than the speed of light. This is a big problem because, according to Einstein’s Theory of Special Relativity, nothing can travel faster than the speed of light.
The same calculations also yield electrons larger than the size of the entire atom–another big problem. Electrons are actually a minute part of atoms. While physicists believe that spin is some kind of rotating motion, it seems to be something other than twirling around the particle’s axis.
The quantum spin of the electron creates a magnetic field. Each electron carries a single negative charge. According to the Maxwell’s Law of Electromagnetism, a charged particle which rotates creates a magnetic field. So, due to its spin, the electron acts like a little magnet with a north and south pole.
In a metal such as iron, the electrons can be aligned so that their north poles all point in the same direction. When this happens, the iron is magnetized; it becomes a magnet. A few other metals, like cobalt and nickel, are also subject to having their electrons aligned in this way, and thus, becoming magnets.
Most other materials have electrons with north poles pointing every which way and cannot be aligned like in iron. Magnetic fields that point every which way cancel each other. So, most materials are not subject to being magnetized.
Quantum Spin is quantized. When measured, spin has two discrete states, up or down (or alternatively, left or right). It’s never measured as either being between nor traveling between the two states. The Schrodinger Wave Function gives the probabilities that, when detected, a particle will be in the up state versus the down state (or left versus right).
Spin is an inherent property. Particles are “born” spinning; it’s an inherent property like the mass or negative electric charge of an electron.
Particles with Spin 1, Spin ½, Spin 0, and possibly even Spin 2. Different types of fundamental particles have been assigned different Spin Numbers: 0, ½, 1, 2…. Note, that these are assigned only to fundamental particles. The spin of composite particles like protons and neutrons seems less clear.
Sometimes people say that Spin 1 means that the particle rotates once, 360°, before returning to its original state; and Spin ½ means it rotates twice, 720°, before returning to its original state!
Another description of what’s going on is based on imagining walking around the electron and being able to see it—no chance of that! But, let’s say you could. You would have to walk around twice (720°) to see the electron in the same orientation as when you started walking.
However, as physicists don’t know the physical meaning of spin, the Spin Numbers are most accurately described at this time (2017) as simply just that: numbers. They are numbers that fit the equations that have been found to match the behavior of particles in lab experiments.
All force-carrying subatomic particles (bosons) have Spin 1. This includes photons (which carry electromagnetic force), gluons (which carry Strong Force), and W and Z bosons (which carry Weak Force).
Matter particles (fermions), like electrons and quarks, have Spin ½.
The Higgs Boson is believed not to spin. It has Spin 0.
No particles have been found with other types of spin. But physicists theorize that if gravitons exist, they would have Spin 2. Gravitons are hypothesized to carry the force of gravity but have not been detected as of yet (2017).
*Source: Seth Lloyd, Programming the Universe; Vintage Books, 2006, New York; p. 91.
**Subatomic particles can come into existence (get “born”) at any time. Any particular particle may have been born when particles started forming about 300,000 years after the Big Bang. Or it may have been born as the result of collisions of other particles or as a result of the decay of another particle. Similarly, it may blink out of existence due to “unfortunate” interactions. In this way, matter is not conserved, even though energy is.