Private Key / Secret Key
In short: A private key, also called a secret key, is a secret piece of data generated by asymmetric (public-key) cryptography and paired with a public key.
A private key, also called a secret key, is a secret piece of data generated by asymmetric (public-key) cryptography and paired with a public key. Data encrypted with the public key can only be decrypted with the matching private key, and in cryptocurrencies the private key is used above all to sign transactions.
Why it matters
Whoever holds the private key controls the funds at the matching address, because only that key can produce a valid signature to move them. If the key is lost, the funds cannot be recovered, and if someone else learns it, they can take the funds. That is why wallets protect keys with seed phrases, encryption or hardware devices, and why a legitimate service never asks you to share your key. When you keep coins on a centralized exchange, the exchange holds the keys to the wallets where those coins are stored.
Example
When you send coins from your wallet, the wallet software builds a transaction and signs it with your private key. Nodes check the signature against your public key and accept the transaction without ever seeing the private key itself. The public key, and the address derived from it, can be shared freely.