Addresses come in two parts - a public key and a private key. The public key can be used to view an address’s balance and transactions, but it cannot be used to make transactions without the private key. The private key is the important part which proves ownership of an account and allows interacting with the Blockchain.
It is free and easy to generate a new address on the Ethereum Blockchain. For instance, https://www.myetherwallet.com/#generate-wallet. The address generated is you public key.