An Ethereum wallet allows you to use the native cryptocurrency of the Ethereum blockchain - Ether (abbreviated to ETH).
The core of an Ethereum wallet is a keypair - both a private and public key. Your Ethereum address is derived from the public key and the private key is used to sign transactions. Both can be backed up conveniently with the seed phrase (12 words). Ethereum wallets interact with Ethereum blockchain to send and receive transactions.
There are several types of wallets, some are connected to the Internet, others are not. Different wallets are used for various purposes such as accessibility or privacy. The key difference between wallets is how private keys are managed. The private key is used as a password to sign outgoing transactions, and anyone who knows it controls the wallet's Ethereum.
The Ethereum address and the associated Ethereum amount are visible on the blockchain. The Bitwala Ethereum-Wallet contains only one ethereum address. An Ethereum address is a hexadecimal string of 42 characters, always starting with a zero and an x, "0x".