Wiping a computer requires clearing information off of the hard drive and overwriting the information on it. Users generally accomplish the first portion of this by reinstalling the operating system, which resets the filesystem, or performing a factory reset to prepare the computer for a new user.
When a computer writes information to a hard drive, it places a pointer to the data's location on a special part of the hard drive and writes the information at that location. However, when the computer deletes the file, it simply deletes the pointer to the data's location and marks the space as free to be overwritten. As a result, the data is still present on the hard drive but is effectively inaccessible. People with access to the hard drive, however, might be able to recover some of this data using special programs.
As a result, completely wiping information from the hard drive requires overwriting it at least once. Even completely overwriting data doesn't necessarily make it unrecoverable, though; hard drives work based on magnetized and non-magnetized regions, and some programs might be able to guess what information that part of the drive used to store based on the strength of this magnetization. As a result, military agencies and other groups who deal with sensitive data often destroy hard drives after writing over the data stored on them multiple times.