Earlier quoted context omitted.
tl;dr Random data may appear to have patterns, but those patterns do not repeat, so they cannot be compressed.
Ah, but they can repeat! There is a finite chance that any sequence of any length will occur in a random sequence. So while a compression alg applied to a very large amount of random data is unlikely to reduce the size, it is quite possible to achieve some compression on smaller blocks.
http://marknelson.us/2012/10/09/the-random-compression-chall...