AuXPoW is the acronym for Auxiliary Proof-of-Work.
Auxiliary Proof-of-Work is a novel consensus mechanism proposed and implemented for the first time in 2013 for DogeCoin, where a blockchain accepts the work conducted on other chains as their own. The concept is simple; miners can use their computational power to participate in mining across multiple chains at once, and whenever a new block is mined the rewards are distributed across the miners. Of course, by spreading their computation across more than one chain the influence they have over the network is reduced but the consistency in rewards and reduction is uncertainties is where AuXPoW excels.
AuXPoW is the mechanism underpinning the process of Merged Mining.