Okay I can't seem to find what a private key truely is, and it's purpose.
I have a private key that is linked to a transaction that is messed up and I would like to take my money back if at all possible
how do I do so?
If that is not the purpose of the private key please explain.
What wallet service are you using? If web wallet then there's a low chance that you can access your private key. In every wallet there is a public key and private key, you only own a wallet address if you have the access on the private key of a particular wallet address/es. And the public key is the one you have to share with others in order to receive bitcoin.
Try to read what is inside
https://en.bitcoin.it/wiki/Private_key.