A quantum state is a complete description of a system within the theory. States can be written in different bases, and the same physical state may look different depending on the choice of basis.

Quantum states can be combined by addition. This means a system can be in a mixture of possibilities such as $a|0\rangle + b|1\rangle$, where $a$ and $b$ are coefficients that determine probabilities.

Spin is an intrinsic form of angular momentum carried by particles like electrons. It is not literally a tiny object spinning like a planet, but it behaves mathematically like angular momentum.

For an electron, spin measurements along a chosen axis can produce only certain discrete outcomes. This is another example of quantization.