Mining is the process through which transactions are verified, and the Bitcoin blockchain is kept intact. The miners essentially work as auditors, verifying bitcoin transactions, making sure that the rules of the Bitcoin protocol are enforced. Through mining, the issue of double-spending is solved, ensuring that you can’t spend your bitcoin more than once, as with physical cash.
The blockchain is the shared public ledger on which the entire Bitcoin network relies. All confirmed transactions - recorded by the miners above - are included in the blockchain. The Bitcoin blockchain is transparent, meaning that everyone can check transactions and if you have the address of a wallet (the account number) you can see every transaction to and from that wallet since it was created. Thanks to this, the balance of every wallet is known in real-time, ensuring the integrity of the blockchain.
Private keys are what you use to prove that you have access to the funds at a certain address on the blockchain, ensuring that the owner of the coins is the one who is trying to use them. Private keys are secret codes available only to the creator of a wallet and are used to sign transactions.