Ethash is the proof-of-work function in Ethereum-based blockchain currencies. It uses Keccak, a hash function eventually standardized to SHA-3. These two are different, and should not be confused. Since version 1.0, Ethash has been designed to be ASIC-resistant via memory-hardness (harder to implement in special ASIC chips) and easily verifiable.
It also uses a slightly modified version of earlier Dagger and Hashimoto hashes to remove computational overhead.
Previously referred to as Dagger-Hashimoto, the Ethash function has evolved over time. Ethash uses an initial 1 GB dataset known as the Ethash DAG and a 16 MB cache for light clients to hold. These are regenerated every 30,000 blocks, known as an epoch. Miners grab slices of the DAG to generate mix-hashes using transaction and receipt data, along with a cryptographic nonce to generate a hash below a dynamic target difficulty.