All Particles have a characteristic called spin. Spin can be thought of as the number of rotations it takes for a particle to return to its initial position. Spin really tells you what a particle will look like from various directions. A particle with a spin of 0 is like a two-dimensional circle--it looks the same from every direction. A particle with a spin of 1 is like an arrow--it takes 1 full revolution or a 360-degree rotation for the arrow to look the same. A particle with a spin of 2 is like a rectangle-it takes a half of a revolution or a 180-degree rotation for the rectangle to look the same. Some particles remarkably have a spin of ½. It takes 2 revolutions, or a 720-degree rotation for these particles to have them look the same.
The known universe can be divided into two groups: particles with a spin of ½ (as well as 3/2) that make up the matter in the universe, and particles with spins of 0, 1 and 2 that give rise to forces and interactions between matter particles (which right now are of no relevance). Particle of spin 0, 1 and 2 also may be directly detected as either light waves or gravitational waves. Spin, as you will see, is very important in the chemistry of an atom as described by the Pauli Exclusion Principle.
The Pauli Exclusion Principle basically states that electrons in the same orbital cannot have the same spin. The spins must be opposite. Since electrons have only one type of spin, ½, this explains why only 2 electrons can occupy the same orbital, because the spin can either be positive, or negative, ½ or - ½.