Zip encoding is a lossless scheme that involves a one-to-one mapping between two large digital numbers. The procedure is lossless in the sense that the mapping is unique and reversible; a computer program "compressed" via the zip mapping can be uncompressed without any loss of information. In effect, the zip approach maps your original file, which is effectively one huge digital number, uniquely onto another digital number in such a way that for most files, the mapped version is shorter than the original—the mapped version has lots of zeros at the beginning or the end that can be omitted when the number is stored as a file. Since the mapping is one-to-one and unique, there must be other files that map badly so that the mapped version is even longer than the original file. But such unfortunate files rarely show up in everyday work and most files map nicely to zipped files that are considerably shorter than the originals.
In contrast, MP3 is a lossy scheme that has been designed explicitly for digital music. Like zip, MP3 involves a mapping process, but this time the mapping is not one-to-one and therefore cannot be reversed perfectly. The mapping is lossy, meaning that some of the original information in the digital music is lost forever when it is turned into an MP3 file. By design, the lost information has a minimal effect on sound quality.
While this toleration of loss is partly responsible for MP3's impressive compression, the rest stems from the fact that normal digital audio is extremely wasteful of space. Digital audio consists of many air pressure measurements, taken one after the other only moments apart. Even though the air pressure rarely changes significantly between any two adjacent measurements, a CD records the entire pressure value for every single measurement. That's like recording entire 5-digit house numbers along a street, even though the numbers barely change from one house to the next. MP3 saves space by recognizing that sequential air pressure measurements probably won't change much.
Answered by Louis A. Bloomfield of the University of Virginia