An ETH address is generated by a cryptographic algorithm that creates a unique string of numbers and letters (a checksum) associated with an Ethereum account. This checksum is used to ensure the accuracy of the address when sending or receiving ETH. The eth address can be thought of as a public key for the Ethereum blockchain. It allows you to send and receive ETH, as well as other Ethereum-based tokens.
When you create an account on an exchange or wallet service, they will generate an ETH address for you. It is important to note that your ethereum address is not your private key. Your private key should never be shared with anyone.