When you want to create a Bitcoin Wallet Address for your Bitcoin Wallet, it is done by generating a Private Key and Public Key.
The Public Key is used to generate Bitcoin Wallet Addresses.
The Private Key is used to prove ownership of the Public Key and generated wallet addresses.
Most web-wallets, like blockchain.info hold and manage your Private Keys for you and secure your account with a password and/or 2-Factor-Authentication. Alternatively you can chose a Bitcoin wallet provider that lets you manage your own Private Keys.