Pauli exclusion principle
/ POW-lee /
Imagine a car park where every parking spot is described by a full address — section, row, bay, and whether you nose in or back in. The rule of this car park is strict: no two cars may share the exact same complete address. Electrons in an atom obey a rule just like this. No two of them can have an identical full set of identifying labels.
Those labels are the four quantum numbers, which between them fix an electron's energy, the shape and orientation of its orbital, and its spin direction. The Pauli exclusion principle states that no two electrons in the same atom can have all four quantum numbers the same. In practice this means an orbital, fixed by the first three numbers, can hold at most two electrons — and only if they spin in opposite directions.
This single rule is why atoms have layered shells instead of all their electrons collapsing into the lowest orbital, and so it underlies the whole structure of the periodic table. More deeply, it applies to all fermions (electrons, protons, neutrons), and it is what keeps matter from being squeezed into nothing — the 'pressure' that holds up white-dwarf stars comes from it.
Helium's two electrons both live in the 1s orbital, which is allowed only because one spins 'up' and the other 'down', making their fourth quantum number differ. A hypothetical third electron could not join them in 1s — there is no remaining spin to distinguish it — so it would be forced up into the next shell.
Two electrons per orbital, and only with opposite spins.
The principle is why atoms take up space and why the periodic table has its row lengths (2, 8, 8, 18, …) — the counts come straight from how many distinct quantum-number sets each shell allows.