A Bitcoin wallet is actually a collection of Bitcoin addresses. A Bitcoin address is essentially an account number. Each Bitcoin address has an associated “private key.” The Bitcoin address can be used to receive bitcoins or see the balance. The private key is needed to spend the bitcoins. see the video about the Bitcoin Private Key.
A wallet can be encrypted. This means the private keys are encrypted so a passphrase is needed to spend any funds. This also means if the passphrase is lost the bitcoins cannot be spent. If an unauthorized person accesses the wallet they cannot spend the funds without the passphrase.
It is also possible to encrypt the entire wallet file. For instance, some users store a wallet backup on a server such as a gmail account.
If the wallet file is unencrypted anyone who gets the file can spend the funds now, or in the future because they will have the private keys.
A wallet can be “watch only” which means you can only receive funds. This is because the private keys are not in the wallet file. the full wallet must exist somewhere, such as a computer not connected to the Internet. In this case bitcoins can be transferred via transactions on a USB or other removable media.
There is also addresses created behind the scenes called “change” addresses. If you have 100 milliBitcoin in your wallet and you send some 20 milliBits the 2 transactions are created. One transaction sends 20 milliBits to the recipient. Behind the scenes your wallet creates a new address in your wallet. A second transaction is created that sends 80 milliBits to yourself using this newly creates address.