1. The compacting of files to save storage space and reduce transfer time. Compression uses algorithms such as Lempel-Ziv, LZW and Huffman coding. From Linux Guide @FirstLinux

2. The reduction of a file's size by means of a compression program. The two types of compression are loassless compression and lossy compression. In lossless compression, the compression process allows for subsequent decompression of the data with no loss of the original data. Lossless compression is used for program and dat files. Lossy compression, in which the compression processes remove some of the data in a way that is not obvious to a person using te data. Lossy compression is used for sounds, graphics, animations, and videos. Many modems offer on-the-fly compression, and often use the MNP5 or V.42bis protocols. From QUECID

3. Since encrypted data is essentially random, you cannot compress it. This defeats networking standards designed to automatically encrypt traffic (such as dial-up modems). Therefore, data must be compressed before it is encrypted. For this reason, compression is becoming an automatic feature to most encryption products. The most often used compression standard is gzip and its compression library zlib. From Hacking-Lexicon