Merge mining or merged mining is the process of mining more than one blockchain simultaneously. This is possible for some proof-of-work (POW) chains, where a miner puts the same hash power to work creating blocks on multiple chains and earns the associated rewards on each of them, without having to pay separate energy costs for each. Here, I explain the ideas behind merge mining.
For a blockchain incorporating the proof-of-work protocol, miners use hash power in order to win the chance of appending their block. For leading chains such as Bitcoin, this is an energy intensive process where each individual hash has a minuscule chance of winning. They need to perform a huge number of hashes to be in with any chance. Where there are multiple proof-of-work chains available, the miner needs to choose which one to contribute his hash rate towards. So long as his hardware is compatible with the specific hashing algorithms used (such as SHA256), he is free to mine on either chain, and switch between them as desired. Usually, it is not possible employ the same hash power simultaneously on both chains. This is because each hash is applied to the block header for the chain in question, so can only be used for solving the POW problem for that specific blockchain. However, if the protocol for all (or, all but one) of the blockchains in question have been designed to specifically to allow for it, then it can be possible for each hash function application to contribute to the proof of work on each chain simultaneously. This is known as auxiliary proof-of-work (AuxPOW).
There are several blockchains that can be merge mined along with Bitcoin. The first such case was Namecoin (NMC), which was created in April 2011 and upgraded in October 2011 to support merge mining. Another example is Rootstock (RSK), which was created in January 2018 and is a sidechain of Bitcoin supporting smart contracts. According to the article The Growth of Bitcoin Merge Mining from October 2020, over 90% of the Bitcoin hashrate is involved in merge mining. This is shown in figure 2 below, borrowed from the same article and showing the proportion of Bitcoin blocks which contain an auxiliary proof-of-work in the coinbase transaction, indicating that it was merge mined along with another blockchain. One notable example not involving Bitcoin is Dogecoin, which is merge mined along with Litecoin, using the scrypt hash function.