Merged mining, if supported by a particular cryptocurrency, gives you an option to earn “extra coins” while mining on more than one blockchain with the same mining algorithm at the same time. The benefit of merged mining is that you do not have to split your hash rate between mining several cryptocurrencies.
Merge mining uses the same hash rate to work on two blockchains at once: the original blockchain (e.g. Bitcoin) and the merge mined blockchain (e.g. RSK or NMC). Every share your miner contributes counts towards the total hash rate of both currencies, and as a result they are more secure. Moreover, you will receive the reward for finding blocks on both of them.
For more technical information regarding merged mining, please read here.