Why do we hiccup?

Hiccup is also called as neuroaccoustic diafragmacontractions and some people call hiccups as hiccoughs.

With the contraction of diaphragm by spasm (diaphragm is a muscular sheet that separates chest and abdominal cavity) the inhaling of air is stopped suddenly. The gap in the vocal cords reduce during the contraction of diaphragm which causes a hiccup and this process is repeated by spasm after few minutes.

CAUSES OF HICCUPS
It can be caused due to the full stomach like eating too much food, smoking, drinking too much of alcohol, excitement, anxiety, stress and it is caused due to the gas problem in the stomach. Sometimes it is also caused due to empty stomach. In many people hiccups occur because of eating hot meal and cold drink at the same time, spicy food, eating very hastily, laughing and coughing.

MORE INFORMATION
The phrenic nerves control the movement and sensation of the diaphragm. Any irritation to these nerves induces a spasm of the diaphragm. This spasm causes a person to take a short, quick breath that is then interrupted by the closing of the epiglottis (a flap that protects the glottis, the space between the vocal cords). The sudden closing creates the sound we all know as a hiccup.
So, hiccups are the result of diaphragm spasms. But what causes the irritation that leads to the spasm? There are only a few culprits for common hiccups, which usually disappear within a few minutes. One of the main irritants is a full stomach -- a result of swallowing too much food or air. A distended stomach pushes against the phrenic nerves of the diaphragm, increasing the possibility of irritation and, therefore, hiccups. A full stomach of spicy food can do double damage -- hot foods can be especially irritating to those nerves. As any smoker on a bender can tell you, excess smoking and drinking alcohol can also cause hiccups. A rapid temperature change outside or inside your stomach, from a cold night or a hot beverage, can be irritating enough to induce hiccups. Finally, emotions -- shock, excitement and stress -- can also trigger a hiccup fit.
Persistent and intractable hiccups can have more serious causes. There are hundreds, from hysteria to heart attacks, but most fit into one of five categories: central nervous system problems, metabolic problems, nerve irritation, anesthesia or surgery, and mental health issues. Because these causes are so varied and potentially serious, anyone suffering from hiccups for more than 48 hours should head straight to a doctor.