Compression is the process of converting one representation of data to a representation that uses fewer bits.
Compression is related to prediction: if a datum can be predicted from previous data, you don't actually need to store it. If you really run with this line of thinking, you might regard even human understandings or aesthetics as a form of compression (see Driven by Compression Progress).
There's lots of interesting work around the aesthetics of compression, e.g. ditherpunk, Small File Media Festival, glitch art, web art,