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.
Notably, the parent blockchain is barely affected as it doesn’t have to go under any kind of technical modification. On the other hand, the auxiliary blockchain needs to be programmed to effectively receive and accept the work of the parent chain. Typically, adding or removing support for merged mining requires a hard fork.
In theory, merged mining can be an interesting method for a small (low-hash) blockchain to increase their security, by leveraging the hashing power of Bitcoin or another bigger chain. This could potentially reduce the possibility of 51% attacks, as long as enough miners agree to adopt merged mining.
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.
Other than that, some say that merged mining decreases security because the economic losses are removed from the process. For instance, Bitcoin miners can use their hashing power on the smaller chain without risking their Bitcoin block rewards. As a consequence, miners would have less reasons to act honestly on the smaller chain.