Bitcoin private address/key (or any other crypto’s private key) is a 256-byte long alphanumerickey that enables you to spend your own bitcoin. Private keys always start with “5” and look like this:
You need to store your private key securely, preferably backed up – because if you lose it or the note gets destroyed you will lose access to your coins.
Your public key (“wallet address”) is generated based on your private key using mathematic cryptography. Public keys start with 1 and can not let anyone know what the private key was.
For long-term Bitcoin holding use wallets that provide you with your private key, because without having access to it you basically entrust your Bitcoin to the person/organization behind the wallet.