Equihash is a Proof-of-Work (PoW) mining algorithm developed by Alex Biryukov and Dmitry Khovratovich at the University of Luxembourg. The idea was proposed in an academic paper: Equihash: Asymmetric Proof-of-Work Based on the Generalized Birthday Problem.
'Asymmetric' in this instance means that the PoW algorithm requires significantly less memory and time for proof verification than it does for proof computation. In other words, it's difficult to compute but easy to verify.
Miners of the cryptocurrencies that use Equihash need to solve an Equihash puzzle using Wagner's algorithm for the Generalized Birthday Problem (GBD) in order to propose a block to add to the end of the blockchain.
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