A private key is a secret digital key with which an owner signs transactions and proves the right to dispose of an address on the blockchain.
In plain words
A public address can be shown: funds are sent to it. A private key must be shown to nobody: whoever knows it controls the funds, and blockchain transactions are irreversible. Most often the key is kept inside a wallet and can be restored from the seed phrase. If “support” asks you to send a key or a phrase, they are fraudsters.
Example. A wallet asks you to confirm a transfer: it signs the transaction with your private key on your device, without passing the key itself to any server.