No compression algorithm works on completely random data. Fortunately (for compressors) there is in practice almost no completely random data sets people care about in the world. Almost all data is corrolated in some way. In pictures you can do a good job of predicting the colours of neighbouring pixels (they will, most of the time, be a similar colour).

In this case they are making use of the fact that JPEGs store a certain mathematical formulation of a picture. It turns out JPEG doesn't store that mathematical formulation very well, so you can squash it loselessly into a better formulation, then later turn it back into the original JPEG.