A cryptographic key used to derive public keys and sign transactions
Private keys come in a variety of forms ranging from alphanumeric strings to a pass-phrase. Regardless of form, the functions of a private key is identical: to generate public keys for receiving funds, and to sign transactions for spending funds. A transaction that is not signed cannot be completed and funds will remain where they are.
Loss of a private key means permanent loss to the funds that are in the addresses associated with the private key. Conversely, anyone who has a private key has full control of all the funds in the corresponding addresses and can send the funds freely