I see it that prediction is a form of compression.

Say you have a computer file composed of two parts, the first represents the setup of an experiment, and the second is the data produced by the experiment.

If you have a good theory relating to this type of experiment, then you can predict much of the second part of the file. So you only need to store the first part and possibly some corrections to the least significant bits of some of the parts of the second part of the file.

Thus with good prediction, you can compress this type of file.