Yes, Ethereum has a testnet. The Ethereum testnet is called Ropsten. Ropsten is a proof-of-work testnet that mimics the Ethereum mainnet. The main difference between Ropsten and the mainnet is that Ropsten has lower security since it is easier to mine blocks on Ropsten.
This makes Ropsten less secure for applications that require high security, such as cryptocurrency wallets. However, Ropsten is useful for developers who want to test their applications on a live network without risking losing real Ether.