What do the subscripts 1/2 and 3/2 for the p-orbitals refer to? What does $p_{1/2}$ and $p_{3/2}$ mean when referring to electron configuration?

I've seen sub shells and I'm assuming it has something to do with spin. I am asking this in regard to the  $8p_{1/2}$ and  $8p_{3/2}$ shells and the way they get filled at different energy levels?
Essentially, this derives from Dirac’s relativistic quantum mechanics.

In nonrelativistic quantum mechanics—the Schrödinger equation that you are probably highly familiar with—p orbitals are triply degenerate while d orbitals are 5-way degenerate. However, nonrelativistic quantum mechanics does not include the electronic property known as spin unless it is introduced in a separate step.

Dirac’s relativistic quantum mechanics solves this problem by introducing $c$ as a finite constant. Almost magically, his equations directly result in a quantum number for the spin, $\vec s$. However, the result is that the azimuthal quantum number no longer behaves like a true quantum number (i.e. it no longer describes stationary states) but thankfully the sum $\vec j = \vec l + \vec s$ does. Therefore, instead of considering just one $\vec l$ as a descriptor to decide between s, p and d orbitals, we are stuck with $\left |\vec l - \vec s\right |$ and $\left | \vec l + \vec s\right |$. For $\vec l = 1$ (a p orbital) this gives us the values of $\vec j = \frac12$ and $\vec j = \frac32$. There are two p orbitals of the $\mathrm p_\frac32$ type and one of the $\mathrm p_\frac12$ type. These are no longer degenerate, i.e. $\mathrm p_\frac12$ has a lower energy than the $\mathrm p_\frac32$ ones.

The orbital of the $\mathrm p_\frac12$ type happens to be spherical in nature. For a more thorough background, I recommend Nicolau’s extensive answer which I mostly paraphrased in the above paragraphs and which contains links to further materials.