Using a digital cable of at least 1.5m in length dramatically reduces the effect of signal reflection (from the receiver back to the transmitter) in typical audiophile equipment. Reflection contributes significantly to jitter in the digital signal. And of course jitter reduces the fidelity of digital music.
In a perfect world where the impedance of the digital source transport (transmitter), transmission line (all wiring, cables, and connectors in between), and the input receiver (DAC) are all identically matched at the S/PDIF standard of 75 ohms, signal reflection is not an issue. But the reality is that this is almost impossible to achieve, particularly in the transmission line.
The choice of 1.5m is just a practical guideline since no one wants a cable in their system that is too long.
For more technical information on this subject consult the following technical article written by Steve Nugent of Empirical Audio.
Posted in: Digital Cables - Statement Silver S/PDIF