The term lossy is used to describe data compression that does not retain all of the original information. Most lossy compression schemes used for visual or auditory information employs perceptual coding which is based on research on how the human mind processes the "information" it receives through the eyes or ears.
The main advantage of lossy compression is that it reduces the total amount of data required to represent the original information. This typically results in smaller file size or less bandwidth required to transmit the information in exchange for absolute accuracy. One of the earliest widespread uses of lossy compression was for voice communication in telecommunications.
There are parallels in visual technologies such as digital photography and video, with JPEG commonly used for images and MPEG for DVD video.
In systems like MP3 (which is actually an adaptation of the audio layer 3 of the MPEG-1 and MPEG-2 video format), the amount or degree of compression may be user selectable at the time of encoding. The higher the level of compression employed (less data), the lower the quality of the resulting audio.
Other formats include WMA (Windows Media Audio) used in Windows OS, and AAC which is used for iTunes, Apple iOS, YouTube, & Android OS. AC-3 developed by Dolby Labs supports surround formats and is typically used on DVDs.
In music applications; depending on the degree of compression and the discrimination of the listener; the results may be so close to the original that the listener's impression is that it is "the same." In the case of discriminating listeners, the degree of compression often needs to be so low that there is little to be gained by using the compression or is almost the same as a file generated using lossless compression. In a noisy environment and more casual listening; moderately compressed files can often provide satisfactory results.
One other important consideration is signal processing. The encoded signal is typically decoded to linear PCM format for processing; and applying signal processing to even decoded compressed files will generally produce inferior results compared to processing the audio prior to lossy data compression.