It appears I cannot find anything that adequately explains Christoffel Notation and what it means. All I know is that it is used to describe the affine geometry of spacetime, and by extent in calculating spacetime geodesics; but I've yet to understand how, or how to use it.

The notation is math, mot physics.  https://en.wikipedia.org/wiki/Christoffel_symbols

There are many good books that explain Christoffel symbols. It's not a notation; it's a real object that you need to correct for the fact that your reference directions change depending on the point when you're taking derivatives of vectors.

A very good classic book is Lovelock & Rund:

https://www.amazon.com/Tensors-Differential-Variational-Principles-Mathematics/dp/0486658406

15 hours ago, Anchovyforestbane said:

It appears I cannot find anything that adequately explains Christoffel Notation and what it means. All I know is that it is used to describe the affine geometry of spacetime, and by extent in calculating spacetime geodesics; but I've yet to understand how, or how to use it.

Have a look here:

https://einsteinrelativelyeasy.com/index.php/dictionary/25-christoffel-symbol

Essentially, the Christoffel symbols (of the 2nd kind) tell you how the components of your basis vectors in a given coordinate system change as you move around a manifold. If you want to define a concept of a covariant derivative - which by definition needs to be consistent everywhere on the manifold -, you need to compensate for this change, which is why the Christoffel symbols appear in the definition of the covariant derivative.