What it does is eliminate the structure of the plaintext. Lots of practical crypto implementation attacks depend on plaintext structure, especially in their most naive and straightforward implementations.

A conceptual purist like Colin Percival would argue, correctly, that if there's an attack against a cryptosystem that benefits from knowing the distribution of bytes in the plaintext, that's a damning statement about the cryptosystem itself.

But compression does "break" some exploits.