Bitcoin, being a purely digital currency, can be owned by people by keeping or storing it in files or in a Bitcoin Wallet. Addresses are used to transfer Bitcoins from one wallet to another, and keys are used to secure a transaction.
Keys in Bitcoins are used in pairs. One is a public key, and the other is a private key. The private key is to be kept securely, since it gives you control over a wallet. The keys are stored and controlled by a Bitcoin wallet.
Addresses are alphanumeric strings that are shared for sending or receiving Bitcoins from one wallet to another. The addresses are mostly encoded as Base58Check, which uses a Base58 number for address transcription. A Bitcoin address is also encoded in a QR code for quick transactions and sharing.