From the website:
The reason the Hic-Cup works is that it reliably interrupts the Hiccup Reflexive Arc by naturally influencing the superficially coursing Vagus and Phrenetic nerves. These nerves are known to be involved in the root cause of hiccups. Through the use of natural galvanic action, a mild ionic flow is created that initiates a sub-sensory bio-electric therapy. This means that the “hiccup” nerves are “re-set” by a natural electric current that you cannot feel, and that this reliably ends the distressing spasms.