Data compression is where data is encoded using a compression algorithm, to reduce its size. This can be useful when dealing with large amounts of data, such as for a disk image backup, as it can save significant disk space for backup storage.
Different compression algorithms reduce file size by different amounts. Compressing data requires CPU resources (and hence time) to apply a compression algorithm. There is typically a trade off between how small you can compress a file and how long it takes to compress it. Since disk space has become quite cheap, it is typically best to use a fast compression algorithm to quickly reduce any large (easy to compress) files, but not worry too much about getting the highest possible compression, since this will be quite slow and will typically not provide much benefit.
If you are dealing with a lot of image, audio and video files (e.g. jpeg, mp3 and avi formats), you will get little benefit from compression since these file formats already use compression.
If you want a behind the scenes overview of how compression actually works, Khan Academy have an interesting video ..