A private key is a complex string of alphanumeric characters, often converted in 12 or 24 words(seed phrase). Possession and control of the private key are the basis of the user's control over all means associated with the corresponding Bitcoin address. Therefore, never share your private key with anyone! The private key is, so to speak, the proof that someone is the owner of the Bitcoin he has in his Bitcoin wallet. If you share the private key, somebody else can dispose over your Bitcoin. If the private key is lost, it is lost forever. You may have heard of the stories where individuals lost their Bitcoin. Technically they have not lost their Bitcoin, because they are still stored in the Bitcoin blockchain, as explained previously. They lost access to them, because without the private key they cannot prove to the participants in the bitcoin network that they are the owner of the bitcoin in their wallet anymore. As such, “key management is key” and this comes mainly down to security and the confidence that one has in the custody of the private key. Your private keys should be kept securely in your safe where you keep your other important documents. You should never take a picture of your private key or upload it digitally online.
A public key is used to receive bitcoin. When bitcoin is sent to a public key, only the owner of the corresponding private key will be able to produce a valid signature to spend that bitcoin.
An address is used to receive bitcoin and is represented as a string of letters and numbers. A Bitcoin wallet allows users to generate as many addresses as they require. Wallets also allow users to send bitcoin to a provided address. When bitcoin is sent to an address, only the owner of the private key(s) which derived that address is capable of spending the bitcoin.