Bitcoin, as well as all other major cryptocurrencies that came after it, is built upon public-key cryptography, a cryptographic system that uses pairs of keys: public keys, which are publicly known and essential for identification, and private keys, which are kept secret and are used for authentication and encryption.
Major cryptocurrencies like Bitcoin, Ethereum, and Bitcoin Cash function using three fundamental pieces of information: the address, associated with a balance and used for sending and receiving funds, and the address’ corresponding public and private keys. The generation of a bitcoin address begins with the generation of a private key. From there, its corresponding public key can be derived using a known algorithm. The address, which can then be used in transactions, is a shorter, representative form of the public key.
The private key is what grants a cryptocurrency user ownership of the funds on a given address. The Blockchain wallet automatically generates and stores private keys for you. When you send from a Blockchain wallet, the software signs the transaction with your private key (without actually disclosing it), which indicates to the entire network that you have the authority to transfer the funds on the address you’re sending from.
The security of this system comes from the one-way street that is getting from the private key to the public address. It is not possible to derive the public key from the address; likewise, it is impossible to derive the private key from the public key. In the Blockchain wallet, your 12-word recovery phrase is a seed of all the private keys of all the addresses generated within the wallet. This is what allows you to restore access to your funds even if you lose access to your original wallet. Using the recovery phrase will copy over your private keys to a new wallet, essentially creating an exact replica of your original wallet, complete with used addresses and transaction history.