The Pauli exclusion principle
Only one fermion of a given type is allowed to be in a specific quantum state. A quantum state is a discrete level that can be labeled. The labeling gives information about the spatial characteristics (e.g. the orbit) and the spin of the particle. Two electrons can exist in the same quantum orbital, but only if they have different spin states. No two electrons of the same spin can occupy the same orbital state.
This has major consequences for atomic structure. For instance, if all the electrons in a heavy atom like Uranium could occupy the lowest possible energy orbital (which is also the most compact orbital) that atom would be smaller in size than a light atom, because the Coulomb force provided by the nucleus of the heavy atom would be very large. Because of the Pauli exclusion principle, most of the electrons in a heavy atom must occupy states with larger radii, so a heavy atom is in fact somewhat larger than a light one.