Why do atomic orbitals overlap?

Atomic orbitals overlap because they occupy space.

An atomic orbital is a region in space where an electron is most likely to be found.

It has no definite boundary, as in a hydrogen #1s# orbital below.

As an H atom approaches a Cl atom, its #1s# orbital can overlap with the #3p# orbital of the Cl.

This creates a build-up of electron density in the region between the two nuclei.

The increased electron density attracts the two nuclei and reduces their repulsions.

The result is the formation of a covalent bond between H and Cl.

And as an Na atom approaches a Cl atom, its #2s# orbital can overlap with the #3p# orbital of the Cl.

This again increases electron density between the two nuclei.

But this time, the Cl pulls all the electron density completely away from the Na atom and toward itself.

This forms an ionic bond between Na⁺ and Cl⁻.

Without overlap of atomic orbitals, there would be no such thing as covalent or ionic bonds.

Chemistry would be an uninteresting subject to study.

Here’s a video on atomic orbital overlap.