A private key is a large, randomly generated secret number that mathematically corresponds to a public wallet address. Whoever holds the private key can sign transactions from that address — effectively, whoever holds it controls the funds, regardless of who originally set the wallet up.
Private keys are almost never handled directly by users; instead they're generated and protected by wallet software, and backed up via a seed phrase. Anyone who obtains your private key or seed phrase can move your funds, and no legitimate service will ever ask you to share either.