The diode keeps the transistor from going into saturation, which is the primary cause of the "transistor sound". Placing it within the bias network keeps it conducting, so the smaller signals pass through, but the larger ones are met with more resistance and eventually clipped entirely.
There are other ways, but the diode guarantees that the transistor can never saturate, and also reacts to the input signal differently than say a fixed series resistor would. JFETs also suffer from the saturation problem, so the diode is helpful in those circuits as well.