A private key is a randomly selected 256-bit number within a defined range. From it, software derives a public key. A valid digital signature proves authorization without revealing the private key.
The network does not know a legal owner. It verifies that a spending transaction satisfies the script attached to an output. Possession of the necessary keys is therefore practical control, but more complex scripts may require several keys or conditions.
A key exposed to an attacker cannot be made secret again. Secure systems minimize online exposure, use tested backups and verify recovery. A seed phrase is a human-manageable backup from which many keys can be derived; it is not the same object as one private key.
For the clearest picture, read this entry together with Wallet, Transaction, UTXO, Bitcoin. The reverse links also lead from Transaction, UTXO, Wallet, Taproot.
Must remain secret
Produces verifiable signatures
Loss can make funds unspendable
Seed phrase can derive many keys