Spin in table tennis is simply the rotation of the ping-pong ball makes. The ball can rotate horizontally, vertically, with a bit of angle, or no rotation at all.
The four fundamental type of spins in table tennis are topsin, nospin, sidespin, and underspin. Topspin and underspin are vertical rotations while sidespin is horizontal. A mixed spin can be generated by combining a little bit of these three spins resulting to an angles rotation. No spin generates no spin.
Spin is what separates table tennis from other racket sports such as badminton. While there are essentially just four basic type of spins, a infinite number of mixed spin can be generated. With table tennis being the fastest sport in Earth, you only have a limited type to react and think of the spin.
