Merge mining is the process of mining two or more blockchains at the same time. Generally there is a parent blockchain and an auxillary blockchain both of which use the same proof of work algorithm. In most cases the auxillary chain will have a lower difficulty than the parent block chain.
Merge mining can be used for securing a lower hashrate blockchain or developing a sidechain that does something different than the primary chain.
Some examples that currently exist or are in development are: a blockchain game TownForge, digital assets platform Tari, and a decentralized mining pool (P2Pool).