Only two electrons, with opposing spins, are allowed in each orbital is known as the

Only two electrons, with opposing spins, are allowed in each orbital is known as the Aufbau's principle.

Explanation:

Aufbau's principle states that at the ground state of atom the atomic orbits of lowest energy are first filled by the electrons followed by the atomic orbits of higher energy.

Example:

1s orbit is first filled by the electrons in the opposite spin followed by 2s. Thus, first 1s is filled with 2 electrons in the opposite spin before filling the 2s orbit.