The Punch Drive refers to the technology that allows for interstellar travel in reasonable time periods, by escaping the limits of general and special relativity as they are understood today.
The Punch Drive provides faster than light travel to ships travelling through space. Upon engaging the Punch Drive, the ship passes into jump space. When dropping out of jump space and back into relative time, the passenger experiences a reality wave. It starts with a shudder and then gives the feeling of splitting or spreading as everything visually blurs.
Presumably, more will be revealed about the mechanical workings of the Punch Drive in future novels.
Although Punch Drives are statistically the safest methods of travel in the galaxy, newcasts often sensationalize the mishaps that have happened. Examples of these mishaps are passenger ships forever lost in Punch Space and ships that have met some stray piece of debris during the punch out back to realtivistic speeds and have resulted in horrific remains.