From the Mayo clinic:
"Hiccups are involuntary contractions of the diaphragm — the muscle that separates your chest from your abdomen and plays an important role in breathing. Each contraction is followed by a sudden closure of your vocal cords, which produces the characteristic "hic" sound."
When I worked at Children's Hospital in D.C. a nurse once told me the best way to stop the contractions was to take a deep breath and hold it. Filling the lungs to capacity presses them against the diaphragm forcing it back into a regular rhythm.
Ever so often mine won't cooperate so I take a deep breath and chug some water. That usually does the trick!