What is Pauli Exclusion Principle?

In short

The Pauli exclusion principle says that no two electrons in an atom can have the same set of four quantum numbers. An orbital can therefore hold at most two electrons, with opposite spins.

In simple words

Each electron is described by $n$ , $l$ , $m_l$ and $m_s$ . Two electrons in the same orbital share $n$ , $l$ and $m_l$ , so they must differ in spin: one is $+\tfrac{1}{2}$ and the other is $-\tfrac{1}{2}$ . The principle explains the capacity of a shell, $2n^2$ electrons, and the structure of the periodic table.

Example

An s subshell has one orbital and holds $2$ electrons. A p subshell has three orbitals and holds $6$ . The $n = 2$ shell holds $2 + 6 = 8$ electrons, which equals $2n^2 = 2 \times 2^2 = 8$ .

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