Merged mining refers to the act of mining two or more cryptocurrencies at the same time, without sacrificing overall mining performance. Essentially, a miner can use their computational power to mine blocks on multiple chains concurrently through the use of what is known as Auxiliary Proof of Work (AuxPoW).
The idea behind AuxPoW is that the work done on one blockchain can be leveraged as valid work on another chain. The blockchain that provides the proof of work is called the parent blockchain, while the one that accepts it as valid is the auxiliary blockchain.
To perform merged mining, all the involved cryptocurrencies must be using the same algorithm. For instance, Bitcoin uses SHA-256, meaning that virtually any other coin that uses SHA-256 can be mined along with Bitcoin - as long as the technical implementations are properly done.
However, many developers disagree with such an idea, and claim that merged mining provides a false sense of security. Mainly because a relatively big mining pool that is not particularly dominant on Bitcoin could easily reach 51% hashing power on the smaller chain. A counterargument to this is that if the reward or incentive is good enough to mine this auxiliary chain, it will attract more miners, thus reducing centralization and increasing security.