A private key is a randomly generated secret number that should only be known to the owner of the associated address. Private keys are contained in a wallet and are mathematically linked to the corresponding public keys. A private key can be used to spend the funds that are associated with a specific address and should, therefore, be kept private. Publicly sharing a private key can, and most likely will, result in a loss of funds.
Private keys are generated locally on your Trezor device and never leave the device. Private keys for Trezor devices are generated based on a recovery seed and (optional) passphrase. In addition to creating and signing transactions, private keys can be used in the Trezor Wallet to sign messages from a specific address to prove ownership of that address.