Private key is a keyword or code consisting of many letters which also proves that the private owner of the key has a digital wallet such as ethereum, bitcoin, and so on.
private key is neither a "keyword" nor a "code". a private key is simply a random number that is encoded into a string of certain length depending on the size of the key so it is human readable. this encoding for bitcoin is base58 encoding with a checksum.
technically private key does not prove ownership, the signature that is cryptographically created using the key does that. and you don't prove ownership of a "wallet" but the coins that belong to that key!