Ok, to understand the Christoffel symbol, I hope the notion of curved space and its unification with acceleration as the warping of gravity is also understood as a prerequisite because the aim of this post is not to teach the literal understandings of what you read in popular science books, but rather to break down what gravity is when it is manifestly spoke about in mathematical physics.
Ok... So hopefully you will already know about basics of Euclidean space ie. The coordinates of ordinary flat space as
x + y + z
Algebraically speaking, this can also be written as the powers