The Pauli Exclusion Principle is ket to understanding the nature and structure of the electron cloud around the atomic nucleus, partcularly in atoms more complex than Hydrogen. It dictates that each atom must have a different quantum state in order to exist.
This principle could then explain the number of atoms in each ground state orbit, the types of orbits, their orientation, momentum and so on.
The four quantum numbers are:
n = energy (shell number)
l = angular momentum (subshells)
m = component of orbital angular momentum
s = component of spin angular momentum
The uncertainty principle is important for understanding that an electron does not have an exclusively particle nature. It is in fact a wave-particle.