When you generate a Ethereum wallet using LocalEtherWallet.com, a
private key for that wallet is generated as well. You then need to store
that private key by downloading
the .JSON file where the private keys are stored. There is an encrypted
(Keystore) and unencrypted version of the file. The encrypted version is
decrypted using a password.
Both the private key and the password are stored in the Keystore file.