Electrons are fermions, which means that they obey the Pauli exclusion principle. This principle states that no two fermions can occupy the same quantum state. In other words, two electrons cannot have the same exact set of quantum numbers.

One of the quantum numbers that electrons have is spin. Spin is a measure of the electron's intrinsic angular momentum. Electrons can have either "up" or "down" spin.

The Pauli exclusion principle means that two electrons in an orbital must have opposite spins. This is why there can only be a maximum of two electrons in an orbital.

The Pauli exclusion principle has a number of important implications for chemistry. For example, it explains why atoms have a characteristic number of electrons in their outermost shell. It also explains why some elements are more reactive than others.

The Pauli exclusion principle is a fundamental law of nature that has a profound impact on the world around us.